GeoGebra Classroom

# Estimate the value of π with other circles.

## Does changing the radius change the ratio of perimeter to radius?

12. Select the SLIDER tool. Name it r=1 and change the minimum value to 0. 13. Select the CIRCLE: CENTER & RADIUS tool. Enter r for the radius. 14. Move the slider to make sure that the circle's radius will change with it. 15. Use the POLYGON tool to inscribe a many-sided polygon, and use the DISTANCE OR LENGTH tool to measure its perimeter. 16. In the box below, write the ratio of perimeter to radius (perimeter divided by radius). 17. Change the radius several times, and write the ratio each time.

## What is the difference between an inscribed polygon and a circumscribed polygon?

18. In the applet below, what is the difference between an inscribed polygon and a circumscribed polygon?

## How can they be used to estimate the value of π?

19. Slowly move the sliders from 1 to 94. This will change the number of sides from 3 to 96. How does the perimeter of the inscribed polygon change, and how does the perimeter of the circumscribed polygon change?

## Find Archimedes' estimate for π.

20. Find the average of the two 96-gon perimeters. (Add the two numbers and divide by two.)