Mathematics+and+Multimedia

The objective of the GeoGebra Step-by-Step Tutorial Series is not only to teach the readers how to use the software, but also to suggest how to use GeoGebra in teaching and learning mathematics. Most of the tutorials are (or will be) linked to related articles containing explanations and proofs about the mathematics discussed in the tutorials. Although, it is advisable to follow the tutorial series chronologically, the reader may opt for any tutorial of choice since each tutorial is designed to be independent from each other. The readers may start from any tutorial, and follow it step-by-step even without learning the tutorials prior to it. Unlike other blogs, all the tutorials in Mathematics and Multimedia, as well as all the articles, are constantly updated and modified for further improvement. This series is not yet complete, its arrangement maybe changed from time to time, but rest assured that more tutorials will be posted. ** What's New **
 * Mathematics and Multimedia GeoGebra Step-by-Step Tutorial Series **
 * 1) The GeoGebra 4.0 Sneak Peek Series. A series introducing GeoGebra users to the new version which will be released in August 2011.
 * 2) GeoGebra Applet Central . A collection of my GeoGebra Applets. The blog is open for contributors. Please inform me at mathandmultimedia@gmail.com if you are interested to contribute.

**A. FOR BEGINNERS **  **I. GeoGebra Essentials Tutorial Series ** **II. Basic Geometric Figures Constructions **
 * < [[image:http://math4allages.files.wordpress.com/2010/04/essentialslist-0.png?w=202&h=178 height="178" caption="external image essentialslist-0.png?w=202&h=178"]] || **[|Introduction to GeoGebra] **This is the introduction to GeoGra. It contains discussions of the different parts of GeoGebra and the advantages in using it. It also points you out to the system installation requirements and the website where you can download it. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/essentialslist-1.png?w=209&h=160 height="160" caption="external image essentialslist-1.png?w=209&h=160"]] ||< **GeoGebra Essentials 1 – Locating the Triangle’s Centroid ** This tutorial, we are going to create a triangle and find its centroid or the intersection of its medians. In doing the tutorial, we are going to learn how to use the following tools: use the new point tool, segment between two points tool, midpoint tool, intersect tool and move tool. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/essentialslist-2.png?w=219&h=167 height="167" caption="external image essentialslist-2.png?w=219&h=167"]] ||< **GeoGebra Essentials 2 – Constructing a Rectangle ** In this tutorial, we are going to create a rectangle using the segment tools, the parallel and perpendicular line tools. We are going to learn how to measure the length of segments and angles. In doing the tutorial, we are also going to discuss semi-free objects. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/essentialslist-3.png?w=228&h=185 height="185" caption="external image essentialslist-3.png?w=228&h=185"]] ||< **GeoGebra Essentials 3 – Triangles, Incircles and CircumCircles **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we are going to show that in any triangle, we can always create a circle passing through its three vertices, and we can always create a circle inscribed in it. The circle that passes through the three vertices of a triangle is called the circumcircle of the triangle, while the circle that inscribed in it is called its incircle. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/essentialslist-4.png?w=223&h=167 height="167" caption="external image essentialslist-4.png?w=223&h=167"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Essentials 4 –Angles, Lengths and Object Properties **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we will use GeoGebra to investigate if a relationship exists between the interior angles of a triangle and the lengths of its sides. We are going to learn two new tools – the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Angle // and the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Distance or Length //tool. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/essentialslist-5.png?w=222&h=164 height="164" caption="external image essentialslist-5.png?w=222&h=164"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGEbra Essentials 5 – The Compass Tool and the SSS Congruence **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we will mimic compass and straightedge construction using GeoGebra’s compass, and segment between two points and ray through two points tool. We will use the concept of the SSS congruence; that is, we will show that if the three corresponding sides of a triangle are congruent, then the triangles are congruent. ||
 * < <span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">[[image:http://math4allages.files.wordpress.com/2010/04/essentialslist-6.png?w=237&h=153 height="153" caption="external image essentialslist-6.png?w=237&h=153" link="http://math4allages.files.wordpress.com/2010/04/essentialslist-6.png"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Essentials 6 –Sliders and Rhombuses **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we will construct a rhombus using two sliders – the angle slider and the number slider. The slider the slider tool. A slider (see figure below) is a dynamic graphical representation of a number. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/essentialslist-7.png?w=255&h=160 height="160" caption="external image essentialslist-7.png?w=255&h=160"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Essentials 7– Using the Keyboard Commands **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this post, we are going to learn how to construct mathematical objects using keyboard commands. We will learn how to In particular, we are going to create an equilateral triangle. ||
 * < [[image:http://math4allages.files.wordpress.com/2011/03/geogebraessentials8-1.png?w=259&h=314&h=169 height="169" caption="external image geogebraessentials8-1.png?w=259&h=314&h=169"]] ||< <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 8 – Graphs and their Properties <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we are going to learn the basics about graphing and how to use GeoGebra command to get the critical points and the derivative of functions. We will also learn how to graph trigonometric, exponential, and logarithmic functions. ||
 * < <span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">[[image:http://math4allages.files.wordpress.com/2010/04/essentialslist-9.png?w=278&h=205 height="205" caption="external image essentialslist-9.png?w=278&h=205" link="http://math4allages.files.wordpress.com/2010/04/essentialslist-9.png"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Essentials 9 – Texts and Variables **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we are going to learn how to use the text tool of GeoGebra. We will learn about constants and variables and will learn how to concatenate them in Geogebra codes. ||
 * <  ||< GeoGebra Tutorial 10 – Exporting Your Document ||
 * 1) <span style="list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 10px; padding-left: 20px; padding-right: 0px; padding-top: 0px;">Introduction to Basic Construction: Construction versus Drawing
 * 2) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Basic Construction 1 – Constructing an Equilateral Triangle
 * 3) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Basic Construction 2 – Constructing an Isosceles Triangle
 * 4) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Basic Construction 3 – Constructing a Right Triangle
 * 5) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Basic Construction 4 – Constructing a Square
 * 6) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Basic Construction 5 – Constructing a Rectangle
 * 7) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Basic Construction 6 - Constructing a Parallelogram
 * 8) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Basic Construction 7 – Constructing a Rhombus
 * 9) <span style="list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 10px; padding-left: 20px; padding-right: 0px; padding-top: 0px;">GeoGebra Basic Construction 8 – Constructing a Trapezoid
 * 10) <span style="list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 10px; padding-left: 20px; padding-right: 0px; padding-top: 0px;">GeoGebra Basic Construction 9 – Constructing a Kite

<span style="color: #008000; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">**<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">B. FOR BEGINNERS/INTERMEDIATE USERS ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">I. GeoGebra Intermediate Tutorial Series ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we are going to inscribe a polygon in a circle, increase its number of sides, and see the relationship between the area of the circle and the area of the polygon as the number of sides increases. This strategy was done by mathematicians in ancient time to approximate the area of a circle. || <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">This tutorial is a continuation of GeoGebra Tutorial 14. In this tutorial, we are going to compare the areas of the circle, its inscribed polygon which we constructed in Tutorial 14 and its circumscribed polygon. || <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we are going to construct point //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">A // on a function, and construct a line tangent to the function and passing through //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">A //. We are also going to plot a point whose//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">x //-coordinate is is the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">x //-coordinate of point //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">A // and the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">y //-coordinate is the slope of the tangent line. We are going to get the derivative of the function and relate it to the path of the second point. || . We will manually create the endpoints and the arrows. || <span style="color: #008000; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">**<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">C. FOR ADVANCED USERS ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">GeoGebra Advanced Tutorial Series ** <span style="color: #008000; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">D. MISCELLANY
 * < [[image:http://math4allages.files.wordpress.com/2010/04/01quadrilateral1.png?w=195&h=185 height="185" align="center" caption="external image 01quadrilateral1.png?w=195&h=185"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra ** **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">Tutorial 1 **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;"> – **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">Midpoints and Quadrilaterals  **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will use GeoGebra to investigate the properties of the polygon formed by connecting consecutive midpoints of sides of a quadrilateral. The tools that we will use in this construction are //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">new point //, //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">segment between two points //, //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">midpoint or center //, and //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">polygon, distance tool and angle tool //. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/02-equilateral.png?w=211&h=143 height="143" caption="external image 02-equilateral.png?w=211&h=143"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 2 – Constructing an Equilateral Triangle ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will mimic //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">compass and straightedge // construction by using radii of two congruent circles to construct an equilateral triangle. The tools that we will use in this tutorial are //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">new point //,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">polygon //, //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">circle with **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">center through point ** //. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/03-square1.png?w=167&h=173 height="173" align="center" caption="external image 03-square1.png?w=167&h=173"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra ** **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">Tutorial 3 – Constructing a Square ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">This construction is similar to Tutorial 2, mimicking the compass and straightedge construction. In this construction, we will use a circle and perpendicular and parallel lines to construct a square. The tools that we will use in this tutorial are//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">new point //, //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">circle with center through point //,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">segment between two points //,**<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">perpendicular line // ** and **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">parallel line // **. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/04-graphs2.png?w=278&h=207 height="207" caption="external image 04-graphs2.png?w=278&h=207"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra ****<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">Tutorial 4 – Graphs and Sliders ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we learn how to use the input box to graph linear functions. We will use the sliders to show the effects of the values of //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">m // and //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">b // to the graph of the function //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">y = m x + b //. In this tutorial, you will learn the advantages of GeoGebra over others. The tool use in this tutorial is the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">slider //. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/05-pythagorean.png?w=221&h=168 height="168" caption="external image 05-pythagorean.png?w=221&h=168"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra ** **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">Tutorial 5 – Discovering the Pythorean Theorem ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will investigate the relationship among the area of the squares formed by the three sides of a right triangle. The tool that we will use in this tutorial are //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">perpendicular line //,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">segment between two points //, and**<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">regular polygon // **. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/06-parameterization1.png?w=257&h=208 height="208" caption="external image 06-parameterization1.png?w=257&h=208"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 6 – Parameterization of Area and Length of a Rectangle ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will learn how to write equations, formulas and perform computations in GeoGebra. We will construct a rectangle with a fixed perimeter and a variable length. We will graph the ordered pair (length,area) of a rectangle with a fixed perimeter in the xy-plane and find the dimensions with the maximum area. The tools that we will use in this tutorial are //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">new point //,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">perpendicular line //, //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">parallel line //, and//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">polygon //. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/07-rotation.png?w=184&h=207 height="207" caption="external image 07-rotation.png?w=184&h=207"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 7 – Sliders, Rotation and the Angle Sum Theorem ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will use the slider tool and rotation to replicate triangles, rotate them and show that the angle sum of a triangle is 180 degrees. The tools that we will use in this tutorial are **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">line through two points // **,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> midpoint or center //,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">polygon //, //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">slider //, and **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">rotate object around a point by angle // **. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/08-tracing1.png?w=279&h=170 height="170" caption="external image 08-tracing1.png?w=279&h=170"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 8 – Tracing Graphs of Trigonometric Functions ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will trace paths of points formed by coordinates of the distance **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">d // **traveled by a point along the circumference of a circle. We will graph (d,x) and (d,y) where //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">x // and //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">y // are the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">x //and //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">y //-coordinates of the points . The tools that we will use in this construction are //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">new point //, //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">circle with center through point //, and //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">circular // //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">arc with center through two points //. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/09-translation.png?w=245&h=176 height="176" align="center" caption="external image 09-translation.png?w=245&h=176"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">[|GeoGebra Tutorial 9– Vector and Translation] **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we will use the vector tool to translate a triangle. We will explore the relationship among the coordinates of the pre-image of an object, the object of its image, and the direction and magnitude of the vector. The tools that we will use in this tutorial are //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">new // //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">point //,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> polygon //,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> vector between two points //, //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">translate object by vector //. ||
 * < <span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">[[image:http://math4allages.files.wordpress.com/2010/04/10-trigofunctions.png?w=278&h=165 height="165" caption="external image 10-trigofunctions.png?w=278&h=165" link="http://math4allages.files.wordpress.com/2010/04/10-trigofunctions.png"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra ** **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">Tutorial 10 – Vectors and Tessellation ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will use the strategy that we have learned in the Vector and Translation tutorial to tile a plane with regular octagons and squares. The tools that we will use in this tutorial are //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">new ////<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">point //,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> polygon //,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> vector between two points //,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">translate object by vector //and//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> regular polygon //. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/11-trigofunctions3.png?w=289&h=196 height="196" caption="external image 11-trigofunctions3.png?w=289&h=196"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 11 – Sliders and Graphs of Trigonometric Functions **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we will use the slider to investigate the effects of the parameters//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">a, b, c // and //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">d //in the graph of the sine function//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> f(x) = a sin(bx -c) + d //. We will also explore the cosine and tangent functions of the same form. We will learn how to use check boxes to show and hide the graphs. The tools that we will use in this tutorial are //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">slider // and //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">check box // //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">to show/hide objects //. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/12-pictures1.png?w=200&h=152 height="152" caption="external image 12-pictures1.png?w=200&h=152"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 12 – Pictures and Angle Measures ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will learn how to insert text and picture in GeoGebra. We will use the protractor image to measure the angle formed by two segments. The tools that we will use in this tutorial are line through two points, segment between two points, angle, and semicircle through two points. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/13-latex.png?w=208&h=173 height="173" caption="external image 13-latex.png?w=208&h=173"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 13– How to Use Latex in GeoGebra **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we will learn how to embed Latex in GeoGebra worksheets. Latex is a typesetting program capable of constructing complicated mathematical formulas. It is widely used by mathematicians in creating scientific documents. It can also be embedded in websites and is integrated in many mathematics programs. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/14circle-area-approximation2.png?w=210&h=191 height="191" caption="external image 14circle-area-approximation2.png?w=210&h=191"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 14 – Circle Area Approximation by Inscribed Polygons **
 * < [[image:http://math4allages.files.wordpress.com/2010/04/15-circumscribe.png?w=202&h=158 height="158" caption="external image 15-circumscribe.png?w=202&h=158"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 15 – Tangents, Circles and Circumscribed Polygons **
 * < [[image:http://math4allages.files.wordpress.com/2010/04/16-sliderssequence.png?w=208&h=85 height="85" caption="external image 16-sliderssequence.png?w=208&h=85"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 16 – Slider, Sequence and Segment Division **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we are going to learn how to use the slider control and the sequence command to divide a segment with an arbitrary length into n equal partitions. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra18-11.png?w=210&h=210 height="210" caption="external image geogebra18-11.png?w=210&h=210"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 17 -Tangent and the Meaning of Derivative **
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra181.png?w=240&h=186 height="186" caption="external image geogebra181.png?w=240&h=186"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 18 – Area Under a Curve and the Riemann Sums **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we are going to compare the area of a plane under a curve f(x) = x<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">2 bounded by the x-axis and the line x =1 with the sum of the areas of rectangular partitions under the same boundaries. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra192.png?w=214&h=159 height="159" caption="external image geogebra192.png?w=214&h=159"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 19 – Introduction to Spreadsheet **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we are going to use the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Record to Spreadsheet tool // to record the coordinates of a moving point along the graph of a particular function. We will graph the function f(x) = x<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">2, construct point **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">P // ** with coordinates//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">(a,f(a)) // , where //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">a // is a value from a slider. We will record the coordinates of the traces of **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">P // ** . ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra201.png?w=220&h=162 height="162" caption="external image geogebra201.png?w=220&h=162"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 20 –Spreadsheet, Slider and Curves of Best Fit **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we will use the spreadsheet window to input coordinates of points that will be plotted in the coordinate plane. We will use the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Best Fit Line // tool to construct a line of best fit of the plotted points. Finally, we will also use the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Fitpoly // command and the//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">slider // tool to construct polynomial (with varying degrees) curves of best fit. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra211.png?w=217&h=183 height="183" caption="external image geogebra211.png?w=217&h=183"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 21 – Spreadsheet and Similarity **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we will construct a constant number //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">k //, in the form of a slider, and see what happens if we multiply the coordinates (//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">x //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">1 ,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">y //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">1 ), (//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">x //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">2 ,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">y //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">2 ) and (//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">x //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">3 ,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">y //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">3 ) of the vertices of our triangle by //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">k. //We will investigate if there is a relationship between the original triangle and the triangle formed whose vertices have coordinates (//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">kx //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">1 ,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">ky //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">1 ), (//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">kx //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">2 ,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">ky //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">2 ) and (//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">kx //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">3 ,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">ky //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">3 ). ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra22.png?w=225&h=139 height="139" align="center" caption="external image geogebra22.png?w=225&h=139"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 22 – Spreadsheet, Vectors, and Matrices **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we are going to explore the relationship between the product of two 2 x 2 matrices. We will set the entries of the factor matrices to integers, and limit the second matrix entries to values of -1, 0, and 1. We will also observe the relationship between their graphical interpretations, known as vectors. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra23.png?w=213&h=151 height="151" caption="external image geogebra23.png?w=213&h=151"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 23– Spreadsheet, Bar Chart and Histogram **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we are going to use the spreadsheet to perform basic data representation. We will plot a frequency table of grouped data and perform basic computations using the spreadsheet window. After the data is completed, we will construct a histogram. ||
 * <  ||< **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">GeoGebra Tutorial 24– Box and Whiskers ** ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra251.png?w=215&h=157 height="157" caption="external image geogebra251.png?w=215&h=157"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 25– The Rolling Circle **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we are going to use GeoGebra in constructing a rolling circle. This way, we would be able to relate the diameter of the circle to its circumference. Moreover, this activity will reinforce the relationship between the angle and radian measure. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra26.png?w=212&h=143 height="143" caption="external image geogebra26.png?w=212&h=143"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 26– Constructing a Cycloid **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> This tutorial is very similar to the Tutorial 25. In this tutorial, we are going to use GeoGebra to construct a cycloid.A cycloid is the curve defined by the path of a point on the edge of circular wheel as the wheel rolls along a straight line. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra27.png?w=200&h=171 height="171" caption="external image geogebra27.png?w=200&h=171"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 27– Animation and Epicycloids **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we are going to rotate a circle about the center of another circle tangent to it using the animation feature of GeoGebra. Along the rotating circle, we will also rotate a point on its circumference about its center (see red point in the diagram). The path of this point is called the epicycloid. ||
 * <  ||< **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">GeoGebra Tutorial 28– Animation and Hypocycloids ** ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra291.png?w=201&h=156 height="156" caption="external image geogebra291.png?w=201&h=156"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 29– Animation, Loci and Radian Measure **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we are going to introduce the concept of radian. We are going to rotate radius //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">AB’ //about point //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">A, // the center of the circle. As the point rotates, point //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">C // goes back and forth from //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">A // to //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">B’ //at the same speed as that of //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">C //. The path of point //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">C //traces forms petals. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra303.png?w=158&h=174 height="174" caption="external image geogebra303.png?w=158&h=174"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 30 – Loci, Roses and Reflections **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we are going to reflect a point on a circle about the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">x // -axis and about the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">y // -axis to form rectangle**<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">ABCD // **. We will construct a segment passing through point**<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">B // ** where one of the endpoints on the center and with length equal to the area of a circle. As we move the point **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">B // **along the the circle, the trace of the end point of the segment (not on the circle’s center) will form a 4-petal rose. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra301.png?w=208&h=189 height="189" caption="external image geogebra301.png?w=208&h=189"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 31 – Paper Folding Simulation **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we are going to use GeoGebra to simulate paper folding. We will represent a rectangular piece of paper with corners //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">**<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">ABCD ** // and drag the upper right corner (vertex //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">**<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">B ** //) anywhere inside the rectangle. We will use the Point in region tool of GeoGebra 4.0 Beta Release (or New Point tool in 3.2) to construct the figure. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/piecewise-i1.png?w=210&h=157 height="157" caption="external image piecewise-i1.png?w=210&h=157"]] ||< **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 10px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 32 – Graphing Piecewise Functions **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> In this tutorial, we are going to use the//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">function // command of GeoGebra to graph piecewise function || [[image:http://s0.wp.com/latex.php?latex=f%28x%29+%3D+%5Cbegin%7Bcases%7D+1-x%2C+x+%5Cleq+1+%5C%5Cx%5E2%2C+x+%3E+1+%5Cend%7Bcases%7D&bg=ffffff&fg=000000&s=0 caption="f(x) = begin{cases} 1-x, x leq 1 x^2, x > 1 end{cases}"]] ||
 * f(x) = begin{cases} 1-x, x leq 1 \x^2, x > 1 end{cases} ||
 * 1) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Advanced Tutorial 1 – Exporting a GeoGebra File to a Dynamic HTML
 * 2) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Advanced Tutorial 2 – Embedding a GeoGebra Applet in Blogger/Blogspot
 * 3) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Advanced Tutorial 3 – Embedding a GeoGebra in a Wiki
 * 4) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">[|GeoGebra Advanced Tutorial 4 – Constructing Customized Tools 1]
 * 5) <span style="list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 10px; padding-left: 20px; padding-right: 0px; padding-top: 0px;">GeoGebra Advanced Tutorial 5 - Constructing Customized Tools 2
 * 6) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Advanced Tutorial 6 – Customizing the GeoGebra Toolbar
 * 7) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Advanced Tutorial 7 – Embedding Form Controls and Javascript
 * 8) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Advanced Tutorial 8 – Random Numbers and Condition to Show
 * 1) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial: Graphs and Sliders Part 2
 * 2) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial: Graphing Functions using GeoGebra
 * 3) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">Can we graph Inequalities in GeoGebra?
 * 4) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">New GeoGebra Tutorials
 * 5) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Video Tutorial 1 – Constructing an Equilateral Triangle
 * 6) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Video Tutorial 2 – Constructing a Square
 * 7) <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">Introduction to GeoGebra Prim Beta


 * B. MISCELLANY **
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">GeoGebra Tutorial: Graphs and Sliders Part 2
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">GeoGebra Tutorial: Graphing Functions using GeoGebra
 * 3) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Can we graph Inequalities in GeoGebra?

** C. EXTERNAL LINKS **
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">GeoGebra Offical Website
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">GeoGebra Download Site
 * 3) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">GeoGebra Forum
 * 4) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">GeoGebra Wiki
 * 5) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">The GeoGebra
 * 6) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Miscellaneous Links


 * D. WHAT’S NEW **
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Introduction to GeoGebra Prim Beta
 * 2) <span style="list-style-position: inside; margin: 0px; padding-bottom: 10px; padding-left: 20px; padding-right: 0px; padding-top: 0px;"> [|GeoGebra 4.0 Beta] (You may want to look at the release notes )
 * 3) <span style="list-style-position: inside; margin: 0px; padding-bottom: 10px; padding-left: 20px; padding-right: 0px; padding-top: 0px;"> GeoGebra 5.0 (with 3d)
 * 4) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">April 2011 Newsletter

** MUTLIMEDIA RESOURCES ** ** Blogging and Web 2.0 ** ** Mathematics Technology Integration ** ** Non Math Free Software/ ** Online Applications ** Resources and References ** ** Teaching/Learning Gadgets **
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|Free tools every math blogger should learn]
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|Top 100 Tools for Learning 2009]
 * 3) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|How to write math equations (integrate Latex) in Blogspot/Blogger]
 * 4) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">How to add a Paypal button to your blog
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|Mathematics in Microsoft Office]
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|Using Google Sketchup in Teaching Mathematics]
 * 3) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Dynamic Statistics with Gapminder
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|Mind Mapping with Freemind]
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;"> [|25 GB of free online storage]
 * 3) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;"> [|Store and publish online for free with Issuu]
 * 4) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;"> [|Store and share your math documents with Scribd]
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|Ask Natural Math and Naturalmath.com]
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|The Amazing Mathematics Illuminated]
 * 3) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|Free Maths Videos at MathsMaster.org]
 * 4) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|Free Technology for Teachers]
 * 5) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|Mind Mapping with Freemind]
 * 6) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|The Best Free Math Tutorial Website]
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|1000+ Free Downloadable Mathematica Demonstrations]
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|Annotating and Zooming with the ZoomIt Software]
 * 3) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|Applets For Visualizing Isometric and Three Dimensional Views]
 * 4) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|Building widgets with Wolfram Alpha]
 * 5) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|Free Mathematics Whiteboard Applet]
 * 6) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|Free Whiteboard Software]
 * 7) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|Google Squared: A new way of searching]
 * 8) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|Investigating Polyhedrons with Poly]
 * 9) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;"> [|You know about ebooks, but have you heard of dbook?]

** MULTIMEDIA TUTORIALS ** ** Audio, Video, and Animation ** ** Compass and Ruler Tutorials ** ** Geometer’s Sketchpad Tutorials ** ** Geonext Tutorials ** ** GnuPlot Tutorials ** ** Google Sketchup ** ** Graphing Software Tutorials ** ** Latex Tutorial ** ** Maxima Tutorials ** ** Microsoft Excel Tutorials ** ** Microsoft Powerpoint Tutorials ** ** Wingeom Tutorials ** <span style="display: block; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">** Wolfram Alpha ** <span style="display: block; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> <span style="display: block; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">** WordPress Tutorial Series ** <span style="display: block; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Screencasting Tutorial: Making a Math Video Lesson using Camstudio
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">How to download math videos from Youtube
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">CaR Tutorial 1 – Constructing an Isosceles Triangle
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">CaR Tutorial 2 – The Midsegment Theorem
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Geometer’s Sketchpad Tutorial 1: Constructing an equilateral triangle
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Geometer’s Sketchpad Tutorial 2: Constructing a Dancing Triangle
 * 3) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Geometer’s Sketchpad Tutorial 3: Graphs and Sliders
 * 4) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Geometer’s Sketchpad Tutorial 4: Constructing a Square
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Geonext Tutorial 1 – Constructing an Equilateral Triangle
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Geonext Tutorial 2 – Constructing a Square
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Gnuplot Tutorial 1 – Graph Basics
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Enhancing your Geometric Drawing using Google Sketchup
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Using Google Sketchup in Teaching Mathematics
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Plotting with Ivan Johansen’s Graph Software
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Latex Tutorial 1: How to embed Latex in blogs and forums
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Latex Tutorial 2: Commonly used Latex Commands
 * 3) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">How to write math equations (integrate Latex) in Blogger/Blogspot
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Maxima Tutorial 1: Numerical Computations
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Maxima Tutorial 2: Algebraic Manipulation and Graphing
 * 3) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Maxima Tutorial 3: Trigonometric Functions and Calculus
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Graphs, Equations and Tables in Microsoft Excel
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Drawing Stunning Diagrams using Microsoft PowerPoint Part I
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Wingeom Tutorial 1 – The Midline Theorem
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Wingeom Tutorial 2 – Constructing an Equilateral Triangle
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">What is Wolfram Alpha and why is it so important?
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Building widgets with Wolfram Alpha
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Introduction to the WordPress Blogging Tutorial Series
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">WordPress Blogging Tutorial 1 – Registering a WordPress Blog
 * 3) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">WordPress Blogging Tutorial 2 – Typing Your First Blog Draft
 * 4) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">WordPress Blogging Tutorial 3 – Publishing your First Blog
 * 5) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">WordPress Blogging Tutorial 4 – Linking posts to other online documents
 * 6) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">WordPress Blogging Tutorial 5 – Embedding Videos and More
 * 7) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">WordPress Blogging Tutorial 6 – Basic Blogging Tips 1
 * 8) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|WordPress Blogging Tutorial 7 – Changing the Theme of Your Blog]
 * 9) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">WordPress Blogging Tutorial 8 – Working with Widgets
 * 10) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">WordPress Blogging Tutorial 9 – Finishing Touches

<span style="color: #008000; margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding: 0px;">**MATHEMATICS RESOURCES** ** NUMBERS **
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Division by 0
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Rational and Irrational Numbers
 * 3) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Counting the Infinite: A Glimpse at Infinite Sets
 * 4) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Is 0.999… really equal to 1?
 * 5) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Prime Series 1: Introduction to Prime Numbers
 * 6) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Prime Series 2: The Intuition Behind the Infinitude of Primes
 * 7) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Prime Series 3: Proof of the Infinitude of Primes
 * 8) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Making Sense of Exponential Growth
 * 9) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Counting the Real Numbers
 * 10) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Young Gauss and the Sum of the First n Positive Integers
 * 11) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Dominoes and Mathematical Induction
 * 12) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|Pythagorean Triple 1: The Infinitude of Pythagorean Triples]
 * 13) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Pythagorean Triple 2: Generating Pythagorean Triples
 * 14) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;"> Large Numbers and One Million
 * 15) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;"> Light Year and the Mathematics of the Stars
 * 16) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">The Geometry of Commutativity
 * 17) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">The Distributive Property
 * 18) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">The Commutativity of Real Numbers
 * 19) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Military Drills and the Closure Property of Real Numbers

** ALGEBRA ** ** GEOMETRY ** <span style="color: #555555; margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding: 0px;">Area Tutorial Series ** TRIGONOMETRY AND PRECALCULUS ** ** CALCULUS ** ** STATISTICS, PROBABILITY AND COMBINATORICS ** ** PROOFS ** ** MATH LITE ** ** MISCELLANEOUS ** ** MATH TEACHING AND PEDAGOGY **
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Operations on Integers – Addition
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Operations on Integers – Subtraction
 * 3) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Operations on Integers – Discovering multiplication and division of integers using patterns
 * 4) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Letters, Variables and Algebraic Expressions
 * 5) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Matchsticks, Linear Relations, and Multiple Representations
 * 6) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Equation of a line: The derivation of y = mx + b
 * 7) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Slope Concept 1 – Understanding the Basic Concepts of Slope
 * 8) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;"> Slope Concept 2 – Slope of the Graph of a Linear Function
 * 9) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;"> Slope Concept 3 – Slopes of Vertical and Horizontal Lines
 * 10) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Arithmetic Sequences and Linear Functions
 * 11) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;"> Derivation of the Quadratic Formula
 * 12) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Geometric Sequences and Series
 * 13) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;"> Why do we reverse the inequality sign?
 * 14) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;"> Why is any number raised to 0 equals 1?
 * 15) <span style="color: #555555; list-style-position: inside; margin: 0px; padding-bottom: 10px; padding-left: 20px; padding-right: 0px; padding-top: 0px;"> Why is zero factorial equals 1 ?
 * 16) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">How to use the summation symbol
 * 17) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;"> Compound Interest and the Irrational Number e
 * 18) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;"> Functions 1: Introduction to the Concept of Functions
 * 19) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;"> Functions 2: Basic Concepts of Functions
 * 20) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;"> Vectors, Parallelograms and Commutativity
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Chess and Axiomatic Systems
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Angle Sum of Polygons
 * 3) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Why is the angle sum of the interior angles of a triangle equal to 180 degrees?
 * 4) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Parallel Lines and Transversals
 * 5) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">The Exterior Angle Theorem
 * 6) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Is there an SSA Congruence?
 * 7) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Making Connections among Pythagorean Theorem, Distance Formula and Equation of a Circle.
 * 8) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">The Algebraic and Geometric Proof of Pythagorean Theorem
 * 9) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Tessellation: The Mathematics of Tiling
 * 10) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Is a square a rectangle?
 * 11) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">The Inscribed Angle Theorem
 * 12) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Demystifying Triangle Inequality
 * 13) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Constructing Segments with Irrational Lengths
 * 14) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|Similarity 1: Introduction to Similarity]
 * 15) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">A Closer Look at the Midpoint Formula
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Area Tutorial 1 - Introduction to the Concept of Area
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Area Tutorial 2 – Area of a Triangle
 * 3) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Area Tutorial 3 – Area of a Parallelogram
 * 4) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Area Tutorial 4 – Area of a Circle
 * 5) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Area Tutorial 5 – Area of a Trapezoid
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|Demystifying Degree and Radian Measures]
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">An Intituive Introduction to Limits
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[[image:http://s0.wp.com/latex.php?latex=%5Cepsilon-%5Cdelta&bg=ffffff&fg=000000&s=0 caption="epsilon-delta" link="@http://math4allages.wordpress.com/2010/03/15/epsilon-delta-definition-of-limits/"]]
 * 3) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[[image:http://s0.wp.com/latex.php?latex=%5Cepsilon-%5Cdelta&bg=ffffff&fg=000000&s=0 caption="epsilon-delta" link="@http://math4allages.wordpress.com/2011/02/27/epsilon-delta-proof-example-1/"]]
 * 4) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Derivative Concept 1: The Algebraic and Geometric Meaning of Derivative
 * 5) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Derivative Concept 2: Derivative in Real Life Context
 * 6) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Derivative Concept 3: Derivative and the Maximum Area Problem
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Introduction to Permutations
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Introduction to Combinations
 * 3) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Binomial Theorem Series 1: Milkshakes, Beads, and Pascal’s Triangle
 * 4) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Binomial Theorem Series 2: The Binomial Expansion
 * 5) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">A Gentle Introduction to Probability
 * 6) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">The Unfinished Game Problem
 * 7) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Using Mathematics to Win the Lottery
 * 8) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Storytelling and Statistics at their finest
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Proof Tutorial 1: Introduction to Mathematical Proofs
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Proof Tutorial 2: Proving the Irrationality of Square Root of 2 by Contradiction
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Funny Math – 10 Steps you Need to Solve a Calculus Problem
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">The Square Root of Three
 * 3) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Why Mathematics Teachers Drink Part 1
 * 4) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Why Mathematics Teachers Drink Part 2
 * 5) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Men, Women, and Mathematics
 * 6) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Amazing Number Patterns
 * 7) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Simba sings math
 * 8) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Math is …
 * 9) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Nature by Numbers: Watch and fall in love with math
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">The Mystery Behind the Proof of 1 = 2
 * 2) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">The Search for Magic Squares
 * 3) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">The definition of Undefined
 * 4) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Is mathematics and exact science?
 * 5) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Eratosthenes and the Earth’s Circumference
 * 6) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Steven Strogatz
 * 7) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Understanding Fermat’s Last Theorem
 * 8) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">[|Making Mathematicians I]
 * 9) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">How do mathematicians greet happy valentines?
 * 10) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">More than 20,000 contest problems and solutions
 * 1) <span style="color: #2970a6; list-style-position: inside; margin: 0px; padding: 0px; text-decoration: none;">Math Exercise, Problem Solving, and Investigation