Objective: to discover the relationship between the perimeter and the diameter of a polygon.

Materials: GSP

Name __________

Period __________

Computer Station ________

1. Constuct circle C. Construct and measure the diameter.

2. Inscribe a square.

a) Select a point on the circle

b) Rotate the point 360/n degrees. (90 degrees for a square. To rotate a point, double click on the center of rotation then click once on the point that is being rotated. Then go to rotate under transform.

c) Continue to rotate the point around the circle.

d) Construct line segments to connect the points.

e) Highlight the polygon interior. Note: polygon interior can be found under the Construct command. All the vertices of the polygon must be selected in order to highlight the polygon interior.

f) Calculate the perimeter.

h) Calculate the ratio of the perimeter to the diameter.

3. Repeat #2 for a hexagon, decagon, and 20-gon. Do the new constructions on top of the previous constructions. Change the color of the polygon interior to enhance the diagram.

polygon	perimeter	diameter	perimeter/diameter
square
hexagon
decagon
20-gon

4. What is the ratio of the perimeter to the diameter approaching?

5. Now calculate the circumference of the circle. What is the ratio of the circumference to the diameter?

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