Question

A question about the plastic number

score 162 · Answer 1 · 2020-03-18 19:03:40

162

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A question about the plastic number

Published on 18 Mar 2020 - 19:03

score 93 · Answer 2 · 2020-03-21 06:25:25

93

Views

How to show that : $4(-1)^nL_n^2+L_{4n}-L_n^4=2$

Published on 21 Mar 2020 - 6:25

score 151 · Answer 3 · 2020-03-28 16:16:13

151

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Show that: $\sum_{n=0}^{\infty}(-1)^{n+1}\left(\frac{F_n}{F_{n+1}F_{n+2}}\right)^2=\frac{1}{\phi^3}$

Published on 28 Mar 2020 - 16:16

score 195 · Answer 4 · 2020-04-01 04:24:36

195

Views

Golden ratio of a circle and square

Published on 01 Apr 2020 - 4:24

score 34 · Answer 5 · 2020-04-21 01:16:54

34

Views

Is it natural or the way that the numerical system was invented that these magics with numbers exist in Nature?

Published on 21 Apr 2020 - 1:16

score 68 · Answer 6 · 2020-04-22 22:52:48

68

Views

How I can prove that the last digit of $1+6^n+2\times 3^n+7^n+4^n+3\times9^{n}+4\times8^n$ is $3$ or $9$?

Published on 22 Apr 2020 - 22:52

score 91 · Answer 7 · 2020-04-23 09:16:26

91

Views

Value of π*φ and π/φ

Published on 23 Apr 2020 - 9:16

score 72 · Answer 8 · 2020-04-23 20:09:28

72

Views

(why) is this ratio the golden ratio?

Published on 23 Apr 2020 - 20:09

score 143 · Answer 9 · 2020-04-26 02:29:49

143

Views

A conjecture concerning Fibonacci

Published on 26 Apr 2020 - 2:29

score 475 · Answer 10 · 2020-04-27 12:19:35

475

Views

On the formula, $\pi = \frac 5\varphi\cdot\frac 2{\sqrt{2+\sqrt{2+\varphi}}}\cdot\frac 2{\sqrt{2+\sqrt{2+\sqrt{2+\varphi}}}}\cdots$

Published on 27 Apr 2020 - 12:19

score 147 · Answer 11 · 2020-04-29 12:57:09

147

Views

How can I construct a Golden Ratio Gauge like this? What shall be the legs of such a gauge?

Published on 29 Apr 2020 - 12:57

score 279 · Answer 12 · 2020-05-07 20:42:15

279

Views

Which of the following numbers is a Fibonacci number; $(A) 75023$ $(B) 75024$ $(C) 75025$ $(D) 75026$?

Published on 07 May 2020 - 20:42

score 249 · Answer 13 · 2020-05-12 12:16:44

249

Views

$\sqrt{2} \ln \pi \approx 1.618033…$, the golden ratio. Why?

Published on 12 May 2020 - 12:16

score 107 · Answer 14 · 2020-06-08 22:08:54

107

Views

Solve Differential Equation $ f^{-1}(x)=f'(x) $

Published on 08 Jun 2020 - 22:08

score 635 · Answer 15 · 2020-06-13 20:38:38

635

Views

Charming approximation of $\pi$: $2\left(\frac{1}{2}\right)^{\phi/2}+2< \pi$, where $\phi$ is the golden ratio

Published on 13 Jun 2020 - 20:38

List Question

A question about the plastic number

How to show that : $4(-1)^nL_n^2+L_{4n}-L_n^4=2$

Show that: $\sum_{n=0}^{\infty}(-1)^{n+1}\left(\frac{F_n}{F_{n+1}F_{n+2}}\right)^2=\frac{1}{\phi^3}$

Golden ratio of a circle and square

Is it natural or the way that the numerical system was invented that these magics with numbers exist in Nature?

How I can prove that the last digit of $1+6^n+2\times 3^n+7^n+4^n+3\times9^{n}+4\times8^n$ is $3$ or $9$?

Value of π*φ and π/φ

(why) is this ratio the golden ratio?

A conjecture concerning Fibonacci

On the formula, $\pi = \frac 5\varphi\cdot\frac 2{\sqrt{2+\sqrt{2+\varphi}}}\cdot\frac 2{\sqrt{2+\sqrt{2+\sqrt{2+\varphi}}}}\cdots$

How can I construct a Golden Ratio Gauge like this? What shall be the legs of such a gauge?

Which of the following numbers is a Fibonacci number; $(A) 75023$ $(B) 75024$ $(C) 75025$ $(D) 75026$?

$\sqrt{2} \ln \pi \approx 1.618033…$, the golden ratio. Why?

Solve Differential Equation $ f^{-1}(x)=f'(x) $

Charming approximation of $\pi$: $2\left(\frac{1}{2}\right)^{\phi/2}+2< \pi$, where $\phi$ is the golden ratio

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