List questions from golden-ratio

Published on 11 Apr 2017 - 23:19

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A conjectured continued fraction for $\phi^\phi$

Published on 12 Apr 2017 - 12:25

214

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What are some numbers/families of numbers, asides from $\Phi$, $\pi$, and $e$ which have interesting algebraic properties?

Published on 23 Apr 2017 - 3:54

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Golden-Ratio Distribution - analogous to Normal distribution

Published on 26 Apr 2017 - 14:46

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How can we show that $\int_{-1}^{1}{1\over x}\sqrt{1+x\over 1-x}\ln\left({1-x+2x^3\over 1+x-2x^3}\right)dx=2\pi arccot\left(2\sqrt{\phi^3}\right)?$

Published on 25 Mar 2026 - 15:52

99

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Golden Rectangle where width is equal to 2 units

Published on 07 May 2017 - 8:17

235

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$a/b < (1 + \sqrt{5})/2 \iff a^2 - ab - b^2 < 0$?

Published on 14 May 2017 - 14:37

232

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What are some alternative ways to represent the golden ratio?

Published on 29 May 2017 - 12:50

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A Matrix With Eigenvalues Equal to The Golden Ratio and the Golden Conjugate

Published on 31 May 2017 - 18:19

48

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Does the golden ratio have infinitely many prime prefixes?

Published on 01 Jun 2017 - 22:45

331

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Is a visual proof to $\varphi = 1 + \tfrac{1}{{1 + \tfrac{1}{{1 + \tfrac{1}{{1 + \,\ddots\,}}}}}}$?

Published on 03 Jun 2017 - 7:11

147

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Egyptian fraction for $\varphi- {F(2n+2) \over F(2n+1)}$

Published on 23 Feb 2026 - 11:10

466

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Partial fractions (Fibonacci system)

Published on 05 Jun 2017 - 17:15

1.3k

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What is the quickest way to calculate $\phi$?

Published on 06 Jun 2017 - 15:33

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Is there a reason why $\log \phi \approx (\log 2)^2$?

Published on 12 Jun 2017 - 15:50

List Question

Solve for n in golden ratio fibonacci equation

A conjectured continued fraction for $\phi^\phi$

What are some numbers/families of numbers, asides from $\Phi$, $\pi$, and $e$ which have interesting algebraic properties?

Golden-Ratio Distribution - analogous to Normal distribution

How can we show that $\int_{-1}^{1}{1\over x}\sqrt{1+x\over 1-x}\ln\left({1-x+2x^3\over 1+x-2x^3}\right)dx=2\pi arccot\left(2\sqrt{\phi^3}\right)?$

Golden Rectangle where width is equal to 2 units

$a/b < (1 + \sqrt{5})/2 \iff a^2 - ab - b^2 < 0$?

What are some alternative ways to represent the golden ratio?

A Matrix With Eigenvalues Equal to The Golden Ratio and the Golden Conjugate

Does the golden ratio have infinitely many prime prefixes?

Is a visual proof to $\varphi = 1 + \tfrac{1}{{1 + \tfrac{1}{{1 + \tfrac{1}{{1 + \,\ddots\,}}}}}}$?

Egyptian fraction for $\varphi- {F(2n+2) \over F(2n+1)}$

Partial fractions (Fibonacci system)

What is the quickest way to calculate $\phi$?

Is there a reason why $\log \phi \approx (\log 2)^2$?

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