Archimedes inscribed polygons
- Author:
- Trent Burchard
- Topic:
- Polygons
Click the slider tool and then use your arrow keys on the keyboard to see what happens as we double the sides our polygon has.
By doubling the number of sides for our inscribed polygon we can use a formula to find the perimeter of a regular polygon with sides of 6, 12, 24, 48, 96, and so on. Start with a hexagon and let the radius of the circle (segment AB) equal 1. Determine the length of segment EB. Notice, EB represents the side length of the next polygon in the sequence.
Using an excel spreadsheet, and a radius of 1, determine the perimeter for each polygon in the sequence. If formulas are used correctly, you should be able to find the perimeter for a 12-sided polygon and then use the "drop down" feature to fill in the rest. Then, taking the perimeter for each polygon and dividing by 2 (the diameter of the circle) we will obtain an approximation for pi. Notice that as we increase the number of sides, the polygon begins to resemble a circle, resulting in an approximation closer and closer to the value of pi.