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Pi was discovered, not invented. It was found, centuries ago, that no matter what size a circle was, the circumference always bore the same relationship to the diameter. They knew, even though they lacked precise measuring tools, that this number was not one which could be expressed as the exact ration of any two numbers. It has been 'refined' down the ages - drawing ever closer to the true figure, but never getting there. As a result, pi is used as a 'shorthand' for a very imprecise figure.

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Q: Why did they invent pi?
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