Scratch

Project Notes

This project calculates approximate values of Pi using only the distance formula by approximating the circle with regular polygons.

This is the technique an ant with a straight ruler might use if he wanted to calculate pi. He walks out from the center in opposite directions until he finds the circle edges to get the diameter.

Then, he divides the circle up into segments. He walks along each segment until he finds the edge of the circle and measures the distance to the last point on the circle, creating a polygon. By adding up the distances along the perimeter of the polygon, he gets an approximate circumference.

Dividing that by the diameter yields an approximate value of pi. The approximation will be more accurate if the polygon has more sides.

There are a couple of substantial inaccuracies in this calculation:

1. The circle is not perfect, it is approximated by a set of pixels.

2. The probe is also not a perfect circle, it is crudely approximated by a set of pixels


But despite that, the ant can get a pretty good result with only 30 sides or so. Not too shabby!

Note that the ant could save a lot of time by measuring one side of the polygon and multiplyiing by the number of sides (since these are regular polygons) but that wouldn't be nearly as much fun to watch!

Credit again goes to Kevin Karplus for his Print Decimal routine.