Archimedes Upper Bound For Pi

The radius of the circle is 1/2 so the circumference of the circle is pi. The circumscribed polygon has perimeter close to pi if the number of sides is large. The perimeter can be calculated with the angle bisector theorem. Then the Pythagorean Theorem can be used along with the angle bisector theorem to find the next perimeter.

 

Gary Rubinstein

 
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