@InertialObservr A fact I think your followers would appreciate.
Pick a random number between 0 and 1. Take it’s reciprocal, then round down. The probability the result is odd is Pi/4.
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I need to make a correction. The probability that it is even is ln(2). Why? Floor(1/x) is even if x is between 1/2 and 1 or x is between 1/4 and 1/3 Or x is between 1/6 and 1/5 and so in. The length of those unions gives you the Taylor expansion of ln(2)
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Ln(2) is the probability it’s odd. 1-ln(2) is probability it’s even. Forget pi/4. I’m typing faster than I’m thinking.
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By similar reasoning, pi/4 is the probability that floor(1/x) is 1 or 2 mod 4
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