What happens if we promote the Golden Ratio φ to a derivative? It turns out that the functions satisfying the "golden differential equation" are exponentials of the Golden Ratio!pic.twitter.com/vNEaZEoeLk
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That's not a unique property of the Golden ratio though. The statement holds for every zero of a real polynomial, i.e. every complex number. So yes, it's neat, but not because of the Golden ratio involved!
i'm not sure i agree with that.. a second order homogenous differential equation has a unique characteristic polynomial, and there is only one polynomial equation for φ
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I guess one can argue that the ODE looks nice, which comes from the polynomial having integer coefficients. But: Many other algebraic numbers have cool ODEs associated with them, not just phi.
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yea! i actually got curious and exploring that now.. except i'm looking at recursively defined functions
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Only one (monic) polynomial with *rational* coefficients, at any rate.
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