Dice Rolling Simulation

1.) Roll the dice 20 times by clicking the command button and record the sums. What do you observe?
2.) Roll the dice 30 times more. Is your observation still the same?
3.) Which of the sums has the most number? has the least number?
4.) Explain why this is so.

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

I have written about dice rolling,  and experimental and theoretical probablity in Math and Multimedia.

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Random segments on a grid

Problem: Suppose the endpoints of a line segment are determined by the uniform random selection of two points on a 12 x 12 grid in a square. Now repeat this to randomly determine a second line segment. What is the probability that these two segments cross, i.e. have a point in common?

To Simulate: Move the slider to select speed.

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

Download GGB file at GeoGebra Tube.
More than 50 GeoGebra tutorials at Math and Multimedia

Perpendicular to a point on the line

Given a point on a line, construct a line perpendicular to it.


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Download file from GeoGebraTube (see download link at the bottom right).

More than 50 Step by Step GeoGebra Tutorials at Math and Mutlimedia

Properties of Similar Triangles

1.) Check the check boxes and see the relationship between the triangles. What do you observe?
2.) Move the verticles of the smaller triangle. Are your observations still the same?
3.) Make a conjecture about your observations.

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There is a discussion about similar triangles and their properties (part 1 and part 2) in my main blog, Mathematics and Multimedia.

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Constructing Similar Triangles

1.) Move the slider to the right to construct a triangle similar to triangle ABC.
2.) Using the tools on the toolbar to compare the measure of the interior angles, side lengths, and areas of the two triangles. What do you observe?

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3.) Move the vertices of triangle ABC. Do your observations still hold?
4.) Make conjectures based on your observations and prove your conjectures.

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Translation of Function

Move vector u to translate the function.

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Parallelogram Area Proof

1. Move H to the rightmost part of the segment.
2. What is the relationship between the area of the parallelogram to the area of the rectangle? Why?

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This applet illustrates that the area of a parallelogram is equal to the product of its base and its altitude.

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The Kite Polygon

Move points A, D, or O to change the shape and position of the kite.

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A kite is a parallelogram whose four sides can be grouped into two pairs of equal-length sides that are next to each other.

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Constructing an Equilateral Triangle

Move the Step slider to the right to perform construction an equilateral triangle.

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