1. Select the CIRCLE: CENTER & RADIUS [icon]https://www.geogebra.org/images/ggb/toolbar/mode_circlepointradius.png[/icon] tool. Click wherever you want the center to be, and then enter a radius of 0.5 so that the diameter will be 1.[br]2. Zoom in so that you can easily see the circle.[br]3. Select the POLYGON [icon]https://www.geogebra.org/images/ggb/toolbar/mode_polygon.png[/icon] 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.)[br]4. Select the MOVE [icon]https://www.geogebra.org/images/ggb/toolbar/mode_move.png[/icon] tool. Drag the the vertices around to make sure they will stay on the circle. Then arrange them to make a square.[br]5. Select the DISTANCE OR LENGTH [icon]https://www.geogebra.org/images/ggb/toolbar/mode_distance.png[/icon] tool. Click somewhere inside the circle to make a perimeter measurement appear. Record its perimeter below.

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

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