Pi
In Our Time: Science
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The Exhaustion Method of Archimedes
An ancient manuscript was discovered, rediscovered in the Vatican Library. It contains a complete description of this non-rigorous, but essential piece of Archimedes' work. In order to make exhaustion work, you actually have to know what the answer is. You have to have some idea of what it is you're sandwiching. And he had to know that the pi he was talking about, so to speak, for the sphere, was the same pi as the one you get for the circle.
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