If someone asks you for your favorite number and you can't make up your mind, tell 'em 2.254596.... because it's the geometric mean of π and Φ. (I use φ for the "little" golden ratio 0.6180339....)
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hmm.. if I were honest i'd probably have to decide between e as well.. hence my favorite number is ∛πeΦ
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2 cos(π/5) = φ so it's not super surprising.
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you would think that fact about cosine would have something to do with it, but it actually doesn'tpic.twitter.com/jnfOElVDnF
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Prove the e^iπ equality in your next tweet with the Taylor series, or else
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i don't find that proof very satisfying
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I wonder if it also generalizes for other metallic means, i.e. solutions of x² - nx - 1 = 0, without much trig. gymnastics...
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just use complex exponents
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Nice. I think we can get a similar formula with the square exponent "2" replaced by any positive integer n, which would involve the Gamma function (but I don't know if phi will be involved, but maybe something else).
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I don’t know what this is, but it looks pretty
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