Question

Golden Exponent? Tetration

score 197 · Answer 1 · 2026-03-27 15:35:40

197

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Golden Exponent? Tetration

Published on 27 Mar 2026 - 15:35

score 63 · Answer 2 · 2021-04-01 16:50:20

63

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Fibonacci number of local minima in sum of sines

Published on 01 Apr 2021 - 16:50

score 129 · Answer 3 · 2021-04-10 11:00:20

129

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iterated function $a(n) = \lfloor n\phi + 0.5\rfloor$

Published on 10 Apr 2021 - 11:00

score 59 · Answer 4 · 2021-04-20 14:37:39

59

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Is it true that $f(x)^{f(x)^{\dots}}$ with $f(x) = -x^2 -x+1$ converges to the Golden Ratio? Why?

Published on 20 Apr 2021 - 14:37

score 109 · Answer 5 · 2021-05-26 10:57:32

109

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Proof if the digits of the golden ratio are in sequence in the digits of Pi or not

Published on 26 May 2021 - 10:57

score 83 · Answer 6 · 2021-05-27 20:31:48

83

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Prove without induction that the sequence $a_{n}=1+\frac{1}{a_{n-1}}$ $=$ $\frac{F_{n+3}}{F_{n+2}}$ with $a_1=2$ where $F_n$ is the Fibonacci sequence

Published on 27 May 2021 - 20:31

score 335 · Answer 7 · 2026-03-27 00:10:16

335

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Prove that $\int _{-\infty }^{+\infty }{\frac {\mathrm {d} z}{(\phi ^{n}z)^{2}+(F_{2n+1}-\phi F_{2n})(e^{\gamma }z^{2}+\zeta (3)z-\pi )^2}}=1$

Published on 27 Mar 2026 - 0:10

score 112 · Answer 8 · 2021-06-05 17:57:21

112

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$a^2\phi=2$ , what is the value of $2a(\phi+1)$?

Published on 05 Jun 2021 - 17:57

score 303 · Answer 9 · 2021-07-05 15:02:29

303

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Improper integral inequality including the golden ratio and the Sophomore's dream

Published on 05 Jul 2021 - 15:02

score 143 · Answer 10 · 2021-07-08 16:06:09

143

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Fibonacci generating function - quick way to see formula

Published on 08 Jul 2021 - 16:06

score 255 · Answer 11 · 2021-07-30 06:44:23

255

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Estimating golden ration by simulation

Published on 30 Jul 2021 - 6:44

score 133 · Answer 12 · 2021-08-08 20:59:32

133

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Is there a notion of Lucas/Fibonacci sequences beyond adding two numbers at a time, if so where could I read more about that?

Published on 08 Aug 2021 - 20:59

score 108 · Answer 13 · 2021-08-24 18:46:35

108

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Why does the golden ratio show up as the solution to these two simultaneous equations?

Published on 24 Aug 2021 - 18:46

score 121 · Answer 14 · 2021-08-30 14:22:33

121

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Derive an exact value for the Golden ratio

Published on 30 Aug 2021 - 14:22

score 126 · Answer 15 · 2021-09-05 01:34:58

126

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Rectangles with side lengths proportional to transcendental numbers BESIDES $\varphi$

Published on 05 Sep 2021 - 1:34

List Question

Golden Exponent? Tetration

Fibonacci number of local minima in sum of sines

iterated function $a(n) = \lfloor n\phi + 0.5\rfloor$

Is it true that $f(x)^{f(x)^{\dots}}$ with $f(x) = -x^2 -x+1$ converges to the Golden Ratio? Why?

Proof if the digits of the golden ratio are in sequence in the digits of Pi or not

Prove without induction that the sequence $a_{n}=1+\frac{1}{a_{n-1}}$ $=$ $\frac{F_{n+3}}{F_{n+2}}$ with $a_1=2$ where $F_n$ is the Fibonacci sequence

Prove that $\int _{-\infty }^{+\infty }{\frac {\mathrm {d} z}{(\phi ^{n}z)^{2}+(F_{2n+1}-\phi F_{2n})(e^{\gamma }z^{2}+\zeta (3)z-\pi )^2}}=1$

$a^2\phi=2$ , what is the value of $2a(\phi+1)$?

Improper integral inequality including the golden ratio and the Sophomore's dream

Fibonacci generating function - quick way to see formula

Estimating golden ration by simulation

Is there a notion of Lucas/Fibonacci sequences beyond adding two numbers at a time, if so where could I read more about that?

Why does the golden ratio show up as the solution to these two simultaneous equations?

Derive an exact value for the Golden ratio

Rectangles with side lengths proportional to transcendental numbers BESIDES $\varphi$

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