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The Three Classical Problems
The Greeks found that they couldn't do any of these things. They could, but in trying to do them, they developed all sorts of other techniques and they proved to be very fertile. It was only proven in the 19th century that pi is the number which we now call transcendental - it has a decimal expansion going on infinitely long. And I don't know how many million places it's been calculated to now, Marcus Pomerino's.