If you enjoy fractions, the mysteriously symmetrical 355/113 is an extremely accurate (99.99999%) estimate of pi and was the best humanity had for nearly a millennium. The midpoint puts pi at 3.14185, which is over 99.9% accurate. His final estimate for pi, using a shape with 96 sides, was: He began with hexagons (6 sides) and continued 12, 24, 48, 96 until he’d had enough (ever try to take a square root using fractions alone?). So Archimedes had to slave away with these formulas using fractions. Unfortunately, decimals hadn’t been invented in 250 BC, let alone spreadsheets. And after 17 steps, or half a million sides, our guess for pi reaches Excel’s accuracy limit. After 7 steps (512 sides) we have the lauded “five nines”. Let’s assume pi is halfway between the inside and outside boundaries.Īfter 3 steps (32 sides) we already have 99.9% accuracy. #CALCULATE PI IN EXCEL DOWNLOAD#Starting with 4 sides (a square), we make our way to a better pi ( download the spreadsheet):Įvery round, we double the sides (4, 8, 16, 32, 64) and shrink the range where pi could be hiding. Using the Pythagorean theorem, side 2 side 2 = 1, therefore side = $\sqrt$ and 1, we can repeatedly apply this formula to increase the number of sides and get a better guess for pi.īy the way, those special means show up in strange places, don’t they? I don’t have a nice intuitive grasp of the trig identities involved, so we’ll save that battle for another day.
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