# Dueling Pinwheels

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## Pinwheel

Use the window below to create Dueling Pinwheels!

Create the Pinwheel
1. With the Circle with Center tool, construct a circle.
2. With the Polygon tool, construct a triangle that contains two radii and a chord forming an acute triangle on the inside of the circle. Do NOT use the point that is already on the circle. That point controls the radius of the circle.
3. With the Rotate around Point tool, rotate the triangle 60 degrees. Change the color of the triangle by right clicking on a triangle and choosing settings. Create 6 triangles of different color.
4. To animate the pinwheel right click on one of the vertices of the original triangle that is on the circle. Choose Animation. The point should move around the circle. A Play/Pause button will be created in the bottom left of the screen. Press the animate button to see the pinwheel move!
Translate the Pinwheel
1. Stop the animation if it is on.
2. Hide all the points except for one point on the original triangle with the Show/Hide Object tool.
3. With the Vector tool, create a new horizontal vector above the pinwheel.
4. With the Translate by Vector tool, select the pinwheel and vector. Be sure to adjust the vector in order for the two pinwheels to NOT overlap.
5. Click on the animate button. Both pinwheels should be moving!
Reflect the Pinwheels
1. Stop the animation if it is on.
2. With the Segment tool, construct a horizontal segment below the figures.
3. With the Reflect about a Line tool, reflect the two pinwheels over the horizontal line.
4. Click on the animate button. Every pinwheel should be moving.
5. Hide any objects such as extra points and labels.

Explain in detail how the figure would differ if you rotated the triangle 45 degrees instead of 60 degrees. How about at 30 degrees? Be very specific about the differences.

Following the original directions from above, but starting with a convex quadrilateral instead of a triangle, construct one animated pinwheel.

How does the animation look different when the original shape is a quadrilateral? Explain in detail. How would the animation look with larger polygons?

1. Create a circle with and inscribed triangle.
2. With the point tool, place a point near the right-hand edge of the page.
3. With the dilate tool, select the pinwheel then the point on the right edge, then enter a value for the dilation factor.
4. With the move (arrow) tool move the point around.
5. Try other dilation factors.

Describe what a dilation is in detail. How does the point outside affect the dilation? What does the factor do to the dilation?