Geometric representation of the sum of two radicals

This activity is part of the lesson on adding radicals posted at Mathematics for Teaching.

How to construct the figure:

Use the regular polygon tool. Click on two points (endpoints of the diagonal of 2 by 1 unit square in the grid). From then on just click on the diagonals each time to generate the squares.

To type the radical, use the text tool, click anywhere on the grid, check latex in the dialogue window and type \sqrt{5} and you're done.

To change the color, right click on the figure, click color, choose and you're done.

When you are ready click on the file menu and choose new. This will give you a brand new grid to practice constructing the figure.





















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The Rolling Circle

Drag the center of a circle to determine the radius, then drag the slider to roll the circle.




















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1.) What do you observe?
2.) What conjecture can you make based on the relationship of the diameter and the circumference of the circle?

Constructing regular polygons

This is an introductory task for teaching squares and square roots. Click here to view the full sequence of the lesson.

Activity

The pentagon was constructed by clicking the regular polygon tool and then clicking on the grid twice. In the dialogue window, type the number 5 for the number of sides. In the dialogue window you will see information about the polygon.

Your task:
Construct a few more regular polygons using the tool.
Why is it that GeoGebra only needed to know two points and the number of sides to contruct the polygon?






















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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.

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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.