# Dueling Pinwheels

- Author:
- Luke Cioffi

Before you begin, be sure you see the Turn In button at the bottom of the assignment. If you don't just refresh the page. You may be asked to log into Google again. This will allow you to submit your assignment in Google Classroom.

## Pinwheel

Use the window below to create Dueling Pinwheels!

Create the Pinwheel- With the
**Circle with Center**tool, construct a circle. - 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. - 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. - 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**

- Stop the animation if it is on.
- Hide all the points except for one point on the original triangle with the
**Show/Hide Object**tool. - With the
**Vector**tool, create a new horizontal vector above the pinwheel. - 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. - Click on the animate button. Both pinwheels should be moving!

**Reflect the Pinwheels**

- Stop the animation if it is on.
- With the
**Segment**tool, construct a horizontal segment below the figures. - With the
**Reflect about a Line**tool, reflect the two pinwheels over the horizontal line. - Click on the animate button. Every pinwheel should be moving.
- 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?

- Create a circle with and inscribed triangle.
- With the
**point**tool, place a point near the right-hand edge of the page. - With the
**dilate**tool, select the pinwheel then the point on the right edge, then enter a value for the dilation factor. - With the
**move**(arrow) tool move the point around. - 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?