+128406 What Alan describes is known as the "method of exhaustion" employed by Atchimedes. He might have been close to discovering Calculus centuries before it was actually discovered. Unfortunately, he was killed by a Roman soldier. But as the saying goes, 'The brutes win in the short term, but the brains prevail in the long term." And Archimedes was one of the brainiest.
+33614 He didn't. He found approximate values for pi.
He calculated upper and lower bounds for pi by first drawing hexagons that just touched the outside and inside of a circle. He then doubled the number of sides until he had polygons with 96 sides on the outside and inside. Then he calculated their perimeters and divided by the diameter of the circle (he probably just used a circle with diameter 1). This showed him that pi must lie between the limits 223/71 and 22/7.
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+128406 What Alan describes is known as the "method of exhaustion" employed by Atchimedes. He might have been close to discovering Calculus centuries before it was actually discovered. Unfortunately, he was killed by a Roman soldier. But as the saying goes, 'The brutes win in the short term, but the brains prevail in the long term." And Archimedes was one of the brainiest.
