![]() ![]() 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. Inside square (not so easy): The diagonal is 1 (top-to-bottom).Outside square (easy): side = 1, therefore perimeter = 4.Whatever the circumference is, it’s somewhere between the perimeters of the squares: more than the inside, less than the outside.Īnd since squares are, well, square, we find their perimeters easily: Neat - it’s like a racetrack with inner and outer edges. ![]() We don’t know a circle’s circumference, but for kicks let’s draw it between two squares: (He actually used hexagons, but squares are easier to work with and draw, so let’s go with that, ok?). But he didn’t fret, and started with what he did know: the perimeter of a square. What’s behind door #3? Math! How did Archimedes do it?Īrchimedes didn’t know the circumference of a circle. Draw a circle with a steady hand, wrap it with string, and measure with your finest ruler.Pi is the circumference of a circle with diameter 1. I wish I learned his discovery of pi in school - it helps us understand what makes calculus tick. Could you find pi?Īrchimedes found pi to 99.9% accuracy 2000 years ago - without decimal points or even the number zero! Even better, he devised techniques that became the foundations of calculus. But what if you had no textbooks, no computers, and no calculus (egads!) - just your brain and a piece of paper. Sure, you “know” it’s about 3.14159 because you read it in some book.
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