# Questions tagged [golden-ratio]

Questions relating to the golden ratio $\varphi = \frac{1+\sqrt{5}}{2}$

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### A question about the plastic number

The plastic number is well known to be the limiting ratio of the Padovan sequence (OEIS A000931), to wit, $$P_n=P_{n-2}+P_{n-3}\\ \lim_{n\to \infty} \frac{P_{n+1}}{P_n}=p$$ However, it is also the ...
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### Comparing $2$ infinite continued fractions

$A = 1 +\dfrac{1}{1 + \frac{1}{1 + \frac{1}{\ddots}}} \\ B = 2 +\dfrac{1}{2 + \frac{1}{2 + \frac{1}{\ddots}}}$ Given the two infinite continued fractions $A$ and $B$ above, which is larger, $2A$ ...
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### Verifying a continued fraction related to $\logφ$.

The continued fraction is the following, $${1+\cfrac{1\cdot 2}{3φ+\cfrac{1\cdot 2}{5+\cfrac{3\cdot 4}{7φ+\cfrac{3\cdot 4}{9+\ddots}}}}}=\frac{2}{3\logφ}\tag{1}$$ Where, $$φ=\frac{1+\sqrt{5}}{2}$$ ...
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### Identifying An Unusual Curve (Parametric) [closed]

NOTE that: The upper boundary (for positive values of $t$) is defined in terms of infinity, that is at $t=∞$. (There is no lower boundary for negative values of $t$.) NOTE. To any re-reading this, I ...