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What is the formal definition of pi?

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What is the formal definition of pi?

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For any circle, dividing the perimeter by its diameter always gives the same answer. It is a transcendental, irrational number, so it doesn’t end, and it doesn’t repeat. In 1706, William Jones introduced the Greek symbol for pi as notation to represent this number. To find more information click here: http://planetmath.org/encyclopedia/Pi.

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