GeoGebra Classroom

# Estimate the value of π with a unit circle.

## Estimate the value of π with a unit circle.

1. Select the CIRCLE: CENTER & RADIUS tool. Click wherever you want the center to be, and then enter a radius of 0.5 so that the diameter will be 1. 2. Zoom in so that you can easily see the circle. 3. Select the POLYGON tool. Click on the circle's circumference in four different places to create a square with its vertices on the circumference. Click on the first vertex to finish the square. (Each time you click, make sure your mouse's arrow icon turns into a hand icon so that the points you create will be anchored to the circle.) 4. Select the MOVE tool. Drag the the vertices around to make sure they will stay on the circle. Then arrange them to make a square. 5. Select the DISTANCE OR LENGTH tool. Click somewhere inside the circle to make a perimeter measurement appear. Record its perimeter below.

## What is the perimeter of an inscribed polygon with 12 sides?

6. Repeat the instructions above, but this time create a dodecagon (12 sides). 7. Zoom in to confirm that each side is shorter than the arc of the circle beside it. 8. What is the perimeter of this 12-sided approximation of a circle?

## What is the perimeter of an inscribed polygon with many sides?

9. Repeat the instructions above with a polygon that has as many sides. (Archimedes used 96). 10. Zoom in to confirm that each side is shorter than the arc of the circle beside it. 11. How many sides does your shape have, and what is its perimeter?