I'm really not a π day hater, but I do roll my eyes when I read articles exclaiming π "goes on forever!" as if that is a rare and notable property that makes it unique among numbers. I mean, 1/3 "goes on forever" too.
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I see. I oughta look this stuff up. (Just noticed that if you plug in x=¼ you get the Leibniz series for pi)
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Indeed, this approach also provides the most natural elementary explanation of Euler's answer to the Basel problem -- that is, to why the sum of the reciprocal squares is [(pi)^2]/6.
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The really crucial point, though, which I sought tacitly to make earlier, is that "pi" should be defined as the constant appearing in "pi*cot(pi*x)." This is the "morally right" place to root our understanding of the number that so many people seem inclined to celebrate today.
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