Nested square root representation of the golden ratio φpic.twitter.com/nYIUqCsw0w
PhD student of Theoretical Particle Physics @UCIrvine l @NSF Fellow l Physics & Math Animations l Patreon: https://www.patreon.com/inertialobserver …
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Nested square root representation of the golden ratio φpic.twitter.com/nYIUqCsw0w
Interesting that π can be expressed with nested square roots too. What’s nested square root of 2, or 3?
lol thank you for following up
So for: c = 1, x = φ c = 2, x = 2 Any other interesting cases?
Well, c=0 is a special case. If you start from any positive value and iterate f(x)=sqrt(x), you converge to 1, but if you start at 0 you obviously stay at 0
But how are we starting from a positive value? Aren’t we starting from zero?
My maths background isn't strong, so someone correct me if I'm talking nonsense, but isn't the idea of a 'starting point' kind of weird here, since the 'initial value' is buried infinitely far in the expression...?
you've got to create a sequence of n_nested roots and take the limit
Wait, isn't there still ambiguity in the nested sqrt notation in what the intended 1st element of that sequence is? It's clear that the sequence is xₙ₊₁ = √(c+xₙ), but less clear what the intended x₀ is
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