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Q&A and generalisation: On fractions and square roots

score 103 · Answer 1 · 2017-12-29 20:38:31

103

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Q&A and generalisation: On fractions and square roots

Published on 29 Dec 2017 - 20:38

score 42 · Answer 2 · 2018-01-09 01:25:00

42

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Show that the linear combination $a\phi_1^n+b\phi_2^n$ is true for $x_{n+2}=x_{n+1}+x_n$.

Published on 09 Jan 2018 - 1:25

score 1.7k · Answer 3 · 2011-03-14 03:14:00

1.7k

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Uses of the 'Golden Ratio'

Published on 14 Mar 2011 - 3:14

score 246 · Answer 4 · 2011-05-27 08:17:59

246

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Transcendentality of the $\log$ of the golden mean

Published on 27 May 2011 - 8:17

score 2.7k · Answer 5 · 2012-02-05 18:54:48

2.7k

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Another way to go about proving the limit of Fibonacci's sequence quotient.

Published on 05 Feb 2012 - 18:54

score 15.4k · Answer 6 · 2012-04-15 23:23:31

15.4k

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How to prove that $\lim \limits_{n\rightarrow \infty} \frac{F_{n+1}}{F_n}=\frac{\sqrt{5}+1}{2}$

Published on 15 Apr 2012 - 23:23

score 1.1k · Answer 7 · 2012-05-18 20:53:22

1.1k

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Approximation for $\pi$

Published on 18 May 2012 - 20:53

score 922 · Answer 8 · 2012-05-31 06:16:43

922

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Ulam's Spiral, Oppermann's diagonals and the Golden Ratio

Published on 31 May 2012 - 6:16

score 985 · Answer 9 · 2012-06-05 12:45:08

985

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Golden parallelepiped

Published on 05 Jun 2012 - 12:45

score 651 · Answer 10 · 2012-06-29 10:06:00

651

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Does this ratio converge to the Golden Ratio?

Published on 29 Jun 2012 - 10:06

score 636 · Answer 11 · 2012-07-05 20:14:43

636

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Solving Fibonaccis Term Using Golden Ratio ConvergEnce

Published on 05 Jul 2012 - 20:14

score 1.5k · Answer 12 · 2012-07-16 20:41:46

1.5k

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Is the continued fraction of the square root of a base $\phi$ (golden ratio) number periodic when the continued fraction is expressed in base $\phi$?

Published on 16 Jul 2012 - 20:41

score 1.1k · Answer 13 · 2012-07-23 23:00:51

1.1k

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The number $\frac{1}{\sqrt{5}}\left[\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^n\right]$ is always an integer

Published on 23 Jul 2012 - 23:00

score 128 · Answer 14 · 2012-09-02 22:23:05

128

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Is it possible to extend phi to higher order polynomials?

Published on 02 Sep 2012 - 22:23

score 225 · Answer 15 · 2012-09-07 04:33:23

225

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Finding the kth n-anacci number

Published on 07 Sep 2012 - 4:33

List Question

Q&A and generalisation: On fractions and square roots

Show that the linear combination $a\phi_1^n+b\phi_2^n$ is true for $x_{n+2}=x_{n+1}+x_n$.

Uses of the 'Golden Ratio'

Transcendentality of the $\log$ of the golden mean

Another way to go about proving the limit of Fibonacci's sequence quotient.

How to prove that $\lim \limits_{n\rightarrow \infty} \frac{F_{n+1}}{F_n}=\frac{\sqrt{5}+1}{2}$

Approximation for $\pi$

Ulam's Spiral, Oppermann's diagonals and the Golden Ratio

Golden parallelepiped

Does this ratio converge to the Golden Ratio?

Solving Fibonaccis Term Using Golden Ratio ConvergEnce

Is the continued fraction of the square root of a base $\phi$ (golden ratio) number periodic when the continued fraction is expressed in base $\phi$?

The number $\frac{1}{\sqrt{5}}\left[\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^n\right]$ is always an integer

Is it possible to extend phi to higher order polynomials?

Finding the kth n-anacci number

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