Pythagorean Theorem Proof

Given congruent squares P and Q, each of which, containing four congruent right triangles.

Move point A to change the size of the rectangle or point B to change the size of the squares.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Questions

1. Show that the white quadrilateral in square P is a square. 
2. Explain why the area of the square in question 1 is equal to the sum of the area of the two white squares in square Q. 
3. Explain why the answers in questions 1 and 2 hold regardless of the shape of the triangles. 

Download Applet

Mathematics and Multimedia Carnival 20

Welcome to the 20th edition of the Mathematics and Multimedia Blog Carnival - Dartboard Edition.  Here are the posts I have collected this month; some from the blog carnival site and some from my RSS Feed.

Before we begin a carnival, let's have some trivia about the number 20.

• The number of sectors in a dartboard.
• The atomic number of calcium. 
• It is the smallest primitive abundant number
• The number of faces of an icosahedron
• Can be written as the sum of the three Fibonacci numbers: 13 + 5 + 2

Now, let the carnival begin!

GeoGebra 4.0 Essentials Series

My apologies. I am quite busy for the past two weeks, and looks like I am going to be busy until the first week of March.  Anyway, for those who had not visited Mathematics and Multimedia recently, the GeoGebra Essentials Series had already been updated to version 4.0. 

The first 10 tutorials in the GeoGebra Intermediate Tutorial Series were also updated last month.  I hope this will help those who want to learn the new version of GeoGebra. 

I am going to resume the revision next week.

New Blog: Mathematical Palette

Hi all. I have been very busy these past days, I hope to be back next week to create more GeoGebra applets.  

One of the reasons that I am busy because I am setting up a new blog titled Mathematical Palette. It's a blog that celebrates mathematical art, beauty, and wonders. I will be discussing non-content mathematics. I will  focus on the connections of mathematics to other fields such as the arts, music, computer science, etc., in an appreciative manner. Math Palette is a light reading blog and is recommended for elementary school and high school students, math lovers, and math haters as well. 

I have written a short description about the blog to give you an idea of what types of posts I am planning to do in the future. I have also already have written three posts.

• Points, Pixels, and Pointillism
• Lines, Planes and Perspectives
• The Mathematics of Chips and Donuts

Let me also make an announcement:
To all math blog carnival lovers, you may submit your entries  on or before February 18, 2012.  The post date is February 20, 2012.

Animation Using Bézier Curves

"A Bézier curve is a parametric curve frequently used in computer graphics and related fields. Bézier curves are also used in animation as a tool to control motion. In animation applications, such as Adobe Flash and Synfig, Bézier curves are used to outline, for example, movement. Users outline the wanted path in Bézier curves, and the application creates the needed frames for the object to move along the path. "
(from Wikipedia)

• Play the animation.
• Drag the points to change the path of the Green Worm. 

Author: Irina Boyadzhiev

Download BézierAnimation.ggb

This applet is based on Jon Ingram's "How to draw Bezier curves" applet.
http://www.geogebratube.org/material/show/id/1803