GeoGebra Applet Central

The Sum of the Cubes of the First N Natural Numbers Dynamic Geometric Proof

2013-05-02T07:16:00.000+08:00

This applet shows a dynamic geometric proof of the formula for the sum of the cubes of the first n natural numbers. Drag the slider “NumberCubes” to create up to seven cubes. Think of each cube as a collection of n nxn square layers of unit cubes. To find a formula for the sum of the cubes of the first natural numbers we will rearrange the square layers. Drag the slider “Rearrange” or press

Octagon to Square Dissection

2013-04-15T09:00:00.000+08:00

The applet below shows the octagon to square dissection. 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 Reference: "Bennett's Octagon-to-Square Dissection" from the Wolfram Demonstrations Project http://demonstrations.wolfram.com/BennettsOctagonToSquareDissection/

Square Root of a Sum? - Geometric Interpretation

2013-04-08T10:37:00.003+08:00

We know that for non-negative numbers Can we apply the same for the sum? In the example below a and b are the legs of a right triangle. According to the Pythagorean Theorem the hypotenuse is Drag to the left the blue point A to rotate the leg AC around point C until the two legs form one segment. Drag to the left the orange point A to rotate the hypotenuse around point B until it

The Sum of the First n Natural Numbers - Dynamic Geometric Proof

2013-03-07T12:31:00.001+08:00

This applet gives a dynamic proof of the formula for the sum of the first n natural numbers. Irina Boyadzhiev, 6 March 2013, Created with GeoGebra Download the file See the general case - Arithmetic Series. Irina's GeoGebra Applets

The Sum of Squares - dynamic proof

2013-03-03T02:28:00.001+08:00

This applet gives a dynamic proof of the formula for the sum of the squares of the first n natural numbers. We start with three times the sum of the squares and rearrange the parts of one of the sums. Click on "Color the third column". Drag the slider to rearrange the parts of the third column. The area of the formed rectangle equals three times the sum of the squares. Click on Show the

Domain and Range of a Function by Flattening to the Axis

2013-01-23T12:25:00.000+08:00

This applet can be used to introduce the concept of Domain and Range of a function by flattening the graph of the function over the coordinate axes. Click on a button to select one of the three functions. Drag the "domain" slider. The graph of the function is flattened to the x-axis. The trace that is left on the x-axis is the domain of the function. Drag the "range" slider. The graph of the

Domain and Range of a Function

2013-01-13T11:56:00.000+08:00

This applet can be used to demonstrate the concept of Domain and Range of a function. Click on a button to select one of the three functions. Drag the "domain" slider. A vertical ray will scan the viewing window and will project the intersection point of the ray and the function to the x-axis. The domain appears as red interval(s) on the x-axis. Drag the "range" slider. A horizontal ray will

Square Octagon Tessellation

2013-01-02T20:00:00.000+08:00

One of the objectives of GeoGebra Applet Central this year is to update the output files of my GeoGebra Tutorial Series. The previous outputs were still in version 3.2. The applet below is the output of GeoGebra Tutorial 10 - Vectors and Tessellation. I just changed the color of the vectors to make it more visible. In this tutorial, the Vector between Two Points tool is used to translate

Year 2012 in Review - The Most Popular Posts

2012-12-31T19:30:00.000+08:00

It's the end of the year and it's time to look back your favorite posts. Below are the most popular posts for 2012 in terms of traffic (Source: Google Analytics). GeoGebraTube: 12000+ applets and counting Pythagorean Theorem Proof Animation Using Bezier Curves Math and Multimedia Carnival 20 The Arithmetic-Mean Geometric-Mean Inequality Deriving the Equation of the Parablola Fibonacci Number

Square Rectangle Tessellation

2012-12-08T16:26:00.000+08:00

The applet below is another tessellation. It is composed of rectangles and equilateral triangles. It is one of the demiregular tessellations. 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

GeoGebra 4.2 Released

2012-12-07T05:12:00.001+08:00

GeoGebra 4.2, the newest version of GeoGebra, is now available for download. Here are the links to know more about the new features. Overview of the New Features The Official Release Notes A more detailed explanation of the Release Notes GeoGebra 4.2 Sneak Peek Series Please visit my GeoGebra Tutorials page to learn about GeoGebra. I will update them to the newest version as soon as

Hexagon Triangle Tessellation

2012-11-27T19:00:00.000+08:00

Move Points A and B to explore the figure. Explain why the figure tessellates. 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 The tessellation above is one of the 8 semi-regular tessellations. Semi regular tessellations are regular tessellations of the plane by two

GeoGebra 4.2 Release Candidate

2012-11-18T07:44:00.005+08:00

The Release Candidate of GeoGebra 4.2 is now available. Several of its new features are explained by Balazs Koren in the official GeoGebra blog. I have also written a Sneak Peek on its new features. The Sneak Peek includes the following topics: Sneak Peek 1: The GeoGebra Window Sneak Peek 2: The Object Properties Sneak Peek 3: Graphics and Layout Sneak Peek 4: Defaults and Advanced Sections

Slope of a Line

2012-10-25T10:32:00.000+08:00

The line below can be changed by dragging the blue points to a different location or by dragging the entire line. Points C and D can be moved along the line, but they cannot change the line. Move C and D along the line and calculate the ratio m= ∆y/∆x=(y2- y1)/(x2- x1) for several different positions of the points. Show the equation of the line and look for a relationship between the

Tessellation 2: Square, Hexagon, Triangle

2012-10-18T19:00:00.000+08:00

The figure below shows that a plane can be tessellated using 3 regular polygons: squares, hexagons, and triangles. 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

The GeoGebra 4.2 Sneak Peek Series

2012-10-08T13:38:00.000+08:00

I have started writing about the new features of GeoGebra 4.2 in the GeoGebra 4.2 Sneak Peek Series. The series will cover the major changes and new features of GeoGebra. As of this writing, there are already three articles in the series. I will update the series from time to time. If all goes well, GeoGebra 4.2 will be released within the year. The GeoGebra for iPad Kickstarter Project has

New GeoGebra Institute Website

2012-09-27T09:33:00.002+08:00

The GeoGebra Institute of Metro Manila has a new website. We have moved some of the applets and have also created a new GeoGebra Primer. We will be accepting contributors from Filipino GeoGebra users starting next month. If you are interested, you may contact me at nismedmultimedia@gmail.com. The GeoGebra Institute of Metro Manila is the first GeoGebra Institute in the Philippines. The

Demiregular Tessellation 1

2012-09-19T20:00:00.000+08:00

Move point A and point B to explore the tessellation. 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 There is no clear definition of what demi-regular tessellations are. Some sources say that there are 14 of them, but give different types. Some also say that there

A journey along the graph of a function - Increasing and Decreasing Functions

2012-09-15T11:51:00.000+08:00

Click the Start button to start the journey of the Tortoise along the graph of the function. When the Tortoise stops, click on him to start the next section of the trip. 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 Irina Boyadzhiev, Created with GeoGebra

Increasing and Decreasing Functions

2012-09-13T12:48:00.002+08:00

Use the check boxes to show/hide the objects and use the slider to move the points. 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 In an increasing function, the value of y-increases as the value of x-increases. On the other hand, in a decreasing function, the value

The Euler Line

2012-09-01T12:55:00.002+08:00

In the figure below, the green, red, and violet 'points' are the orthocenter, centroid, and circumcenter of triangle ABC respectively. Move the points A, B, and C and notice what happens. Use these points to create different types of triangles. What do you observe? This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't

GeoGebra for the iPad Project Needs Your Support

2012-08-21T09:44:00.003+08:00

The International GeoGebra Institute has started a Kickstarter project for the GeoGebra the iPad. The project aims to create an iPad application for GeoGebra. If the project is completed, the GeoGebra iPad app will be available for download (for free) at the Apple Store. Please help us raise $10,000 for the project. For more information about the project, click here.

GeoGebraTube: 12000+ applets and counting

2012-07-14T13:59:00.003+08:00

GeoGebraTube, the official applet repository site of GeoGebra, has now more than 12000 GeoGebra applets after a year it has gone live — thanks to GeoGebraists all over the world. Applets in GeoGebraTube can be downloaded (including the GGB file), embedded in blogs or websites, or shared to colleagues and friends using social media sites. Recently, the site has also allowed Google, Facebook

Sums and Product

2012-06-28T22:07:00.000+08:00

Move the green point to a desired location, and then move the red point and observe what happens. 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.) What do the numbers on the side of the rectangle represent? 2.) What does the number

GeoGebra launches official blog

2012-06-25T17:32:00.003+08:00

GeoGebra recently launched the official GeoGebra blog . Theblog will contain the latest news, tips, tricks, and everything about GeoGebra. According to the administrator, The blog will also feature post contributions fro GeoGebra bloggers all over the world. Recently, GeoGebra is also starting to integrate theorem proving.