Monday, January 21, 2013

Cross to Isosceles Triangle Dissection

Move the Size slider to change the size of the cross and move the slider alpha to the extreme right to transform the figure. 
This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to

The applet above is an example of a dissection puzzle. A dissection puzzle, also called a transformation puzzle tiling puzzle where a set of pieces can be assembled in different ways to produce two or more distinct geometric shapes (Wikipedia). 

The cross to isosceles triangle dissection puzzle above was created by Henry Dudeney in 1897.


"Dudeney's Cross-to-Isosceles-Right-Triangle Dissection" from the Wolfram Demonstrations Project

Wednesday, January 16, 2013

Folding an Ellipse

Paper Folding Activity

1. Draw a circle and draw a point in its interior.
2. Mark a point anywhere on the circle.
3. Fold such that the two points coincide and crease well.
4. Repeat steps 2-3 as many times as you can.

What do you observer about the creases?

Click the Play button on the bottom-left of the applet to simulate the paper folding activity above.
This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to
Note: The green lines represents the folds on the circle.


Thursday, January 10, 2013

GeoGebra Tutorial: Constructing a Cardioid

A cardioid is a curve formed by moving circles. One of the ways to form a cardioid is shown below. In the applet (move the slider to the extreme right), the cardioid is given as the envelope of circles whose centers lie on a given circle and which pass through a fixed point on the given circle. 

This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to

Step by Step Instruction in Constructing the Applet Above

1. Construct point A at (0,0) and point B at (0,1).
2. Construct a circle with center A and passing through B
3. Construct an angle slider and set the minimum number to 0°, maximum number to 360° degrees and increment of 2°.  
4. Construct angle BAB'. To do this, select the Angle with Given Size tool, click on point B and click on point A to display the Angle with Given Size dialog box. 
5. In the Angle with Given Size dialog box, replace 45° with α,  choose counterclockwise button, and then click OK. 
6. Hide the green sector by right clicking it and then clicking on the Show Object from the pop up menu.
7. Now construct a circle with center B' and passing through B.
8. Right click the circle with center B and  click Trace on. 
9. Move the slider and observe what happens. 


Wednesday, January 2, 2013

GeoGebra Tutorial: How to Disable Reflex Angles

In GeoGebra, we use the Angle tool to reveal angle measures.  By default, an angle can measure  up to 360°; howeverthere are instances that we want it to be less than or equal to 180°.  For example, we need to limit the angle measures of the interior angles of a polygon to 180° if we want to find its angle sum. 

In this tutorial, we learn how to disable angles measuring more than 180° but less than 360°.  Such angles are called reflex angles.  To disable reflex angles, do the following:

1. Right click the angle measure (green sector) and click Object Properties to display the Preferences window.

2. In the Preferences window, click the Basic tab.
3. Select 0° and 180° in the Angle Between dialog box and then close the window.