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.

Triangle Angle Sum Proof

Move the vertices of the triangle and move sliders P and Q to the extreme right. What do you observe?




















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


Based on your observations, make a conjecture about the angle sum of a triangle.

There is a tutorial here on how to create the applet above.

Animation, Roses and Radian

Click the Play button located at the lower-left corner of the GeoGebra applet and watch the applet for a while.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

1.)Pause the animation and refresh your browser. Click the Play button again. Click stop when Point C and point B' coincide. ?

2.) How many degrees has B' rotated the first time point B' and C coincide? Refresh the browser and repeat if necessary.

3.)How many petals are formed during the entire rotation of point B' along the circumference of the circle?

4.) Refresh your web browser and complete the petal. Count the number of rotations. What is the relationship between the the number of rotations and the number of petals. Make interpretation about this relationship.

Constructing a Square

This is the output of GeoGebra Tutorial 3 - Constructing a Square from the GeoGebra Step-by-Step Tutorial Series of Mathematics and Multimedia. The GeoGebra ggb file can be downloaded here.

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Move points A and B. What do you observe?

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Can you think of other ways of constructing a square without using the Regular Polygon tool, or the following the tutorial?

Graphs and Sliders

Move the small circles on sliders m and b. What do you observe?




















Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

1. How do the values of m and b affect the appearance of the graph?
2. Suppose, we can increase the value of m and b as much as we can, is it possible to plot a vertical graph?
3. Explain why your observations in 1 are such.

Notes:

1. Click here to download the ggb file.
2. Click here to read the step-by-step tutorial.
3. Click here to go to the Mathematics and Multimedia GeoGebra Tutorial Series.
4. Click here to go to Mathematics and Multimedia

Equilateral Triangle

Drag the vertices of the equilateral triangle below.

1. What do you observe?
2. Can you think of other ways of creating an equilateral triangle?

Notes:

1. Click here to download the ggb file.
2. Click here to read the step-by-step tutorial.
3. Click here to go to the Mathematics and Multimedia GeoGebra Tutorial Series.
4. Click here to go to Mathematics and Multimedia

Quadrilaterals and Midpoints

1. Use the Move tool (leftmost tool) to move the vertices of the quadrilateral. What do you observe?
2. Use the Distance tool to find the distance between the points and move the points. Do your observations hold true?
3. What conjecture can you make based on your observations?
4. Select the Angle tool (right button) and click the interior of the polygon. Does your conjecture still hold?
5.  Challenge: Prove your conjecture.

Notes:

1. Click here to download the ggb file.
2. Click here to read the step-by-step tutorial.
3. Click here to go to the Mathematics and Multimedia GeoGebra Tutorial Series.
4. Click here to go to Mathematics and Multimedia