List questions from golden-ratio

Published on 15 Jul 2023 - 2:55

72

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Explain this proof of Binet's formula?

Published on 29 Aug 2023 - 2:07

196

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Why is the continued fraction [1,1,1,1,1...] equal to ϕ?

Published on 02 Sep 2023 - 22:58

206

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A conjecture for the golden ration via continued fraction $\phi=\frac{1+\sqrt{5}}{2}$

Published on 23 Sep 2023 - 14:22

246

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A cool integral: $\int^{\ln{\phi}}_{0}\ln\left(e^{x}-e^{-x}\right)dx=-\frac{\pi^2}{20}$

Published on 16 Oct 2023 - 23:18

78

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(answered) found the golden ratio in something out of pure luck and want to know if there is any reason?

Published on 22 Oct 2023 - 18:50

176

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Is there a clever way to show that $\sin (\phi+1)<\frac12$?

Published on 04 Nov 2023 - 13:14

111

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Exponential Fibonacci and its recurrence-relation to ϕ.

Published on 26 Mar 2026 - 4:50

109

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Help with a solution this Fibonacci triangle question

Published on 06 Dec 2023 - 17:13

246

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Ways to "milk" the integral $\int^{1}_{0}\ln\left(\phi^{x}-\phi^{-x}\right)\ln\left(\phi\right)dx=-\frac{\pi^2}{20}$

Published on 16 Dec 2023 - 19:33

66

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Triquetra proportions and Golden Mean?

Published on 17 Dec 2023 - 0:36

61

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How is the Gamma function related to the Golden Ratio?

Published on 29 Dec 2023 - 1:44

47

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Maximum absolute value of sum of m n-th roots of unity

Published on 09 Jan 2024 - 2:03

119

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Fibonacci Spiral vs Golden Spiral?

Published on 29 Jan 2024 - 22:28

85

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Can the Fibonacci Spiral be expressed as a polar equation?

Published on 29 Jan 2024 - 23:10

List Question

Is there a graph that satisfies the golden ratio polynomial?

Explain this proof of Binet's formula?

Why is the continued fraction [1,1,1,1,1...] equal to ϕ?

A conjecture for the golden ration via continued fraction $\phi=\frac{1+\sqrt{5}}{2}$

A cool integral: $\int^{\ln{\phi}}_{0}\ln\left(e^{x}-e^{-x}\right)dx=-\frac{\pi^2}{20}$

(answered) found the golden ratio in something out of pure luck and want to know if there is any reason?

Is there a clever way to show that $\sin (\phi+1)<\frac12$?

Exponential Fibonacci and its recurrence-relation to ϕ.

Help with a solution this Fibonacci triangle question

Ways to "milk" the integral $\int^{1}_{0}\ln\left(\phi^{x}-\phi^{-x}\right)\ln\left(\phi\right)dx=-\frac{\pi^2}{20}$

Triquetra proportions and Golden Mean?

How is the Gamma function related to the Golden Ratio?

Maximum absolute value of sum of m n-th roots of unity

Fibonacci Spiral vs Golden Spiral?

Can the Fibonacci Spiral be expressed as a polar equation?

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