Kind of intuitively tells you why Pi lies between 3 and 4 and closer to 3 than 4 :)
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There's also a variant of this with an inscribed circle for calculating pi using Monte Carlo sampling. Math is beautiful!
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This is a quadratic form, so it is more instructive to see that A = (1/2) × tau × r^2, where tau = 2 × pi. https://tauday.com/tau-manifesto#sec-circular_area …
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Pi /4 appears to be interesting
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Astronomy for Dummies: Think you know math? Bode's Law Explained: Ordinal Spacing of Planets, Arnold's Law why the solar-planetary system is mathematically ideal, link: https://www.facebook.com/notes/bill-arnold/bodes-law-explained-of-the-ordinal-spacing-of-planets-round-the-sun/1517144028508921 …pic.twitter.com/6kywi1LxRh
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As thy difficult a problem as finding quadrature of a circle.
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That is an interesting perspective to the formula. Nice
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