easy as 1,2,3.. = easy as πpic.twitter.com/hytWRidqr4
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A nice proof using complex numbers, and also the fact that e^{iπ} = -1. (where we have taken the principal value)pic.twitter.com/MFdFktIOgH
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Nice result but seemed like you skipped a few steps to make it very clear on the LHS.
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indeed the proof is twitter abbreviated
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I really liked this one - had forgotten about it. Thnx!
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Can you derive some of the more efficient formulas for pi using this kind of trick? I'm talking about these: http://turner.faculty.swau.edu/mathematics/materialslibrary/pi/piforms.html … arctangents of small numbers can be quickly computed using the Taylor series.
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Here's a real doozy: π =176 arctan(1/57) + 28 arctan(1/239) - 48 arctan(1/682) + 96 arctan(1/12943) There are other easier ones, but this has arctangents of really small numbers.
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