List questions from continued-fractions

250

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Do all real numbers have a simple infinite continued fraction representation over the integer square roots?

Published on 07 Dec 2019 - 16:40

44

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Can an infinite continued fraction over the irrationals converge to an integer?

Published on 08 Dec 2019 - 4:45

2.4k

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The monster continued fraction

Published on 08 Dec 2019 - 7:27

45

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Solving the continued fraction functional equation $f(x) = g(x) + \frac1{f(x^n)}$.

Published on 11 Dec 2019 - 17:55

100

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Does Khinchin's constant have an analog for nested radicals?

Published on 14 Dec 2019 - 0:09

150

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Numbers with "known" continued fractions

Published on 25 Mar 2026 - 21:22

94

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Continued fraction of the square $\sqrt{n}$ of the form $[a,\overline{k,b}]$

Published on 17 Dec 2019 - 1:41

98

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Convergence of partial quotients of $Q = \dfrac{1!}{1+\frac{2!}{\ddots}}$

Published on 17 Dec 2019 - 20:53

234

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Question about 12-tone musical scale and rational approximations

Published on 23 Feb 2026 - 4:05

456

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Why continued fraction gives initial solution of Pell's equation

Published on 29 Dec 2019 - 4:41

64

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Numbers whose decimal expansions are their own continued fractions.

Published on 30 Dec 2019 - 22:53

151

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Proposition about continued fractions

Published on 31 Dec 2019 - 15:41

47

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How we simplify the term $\frac{a^0}{2}+\frac{a^1}{2\cdot4}+\frac{a^2}{2\cdot4\cdot2}+\ldots+\frac{a^{n-1}+a^nx}{2\cdot4\cdot2\cdot4\ldots}$?

Published on 09 Jan 2020 - 10:38

84

Views

Proof of Binet's formula continued fraction

Published on 10 Jan 2020 - 12:55

137

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Explanation/Prove for this Continued fraction Algorithm

Published on 13 Jan 2020 - 17:37

List Question

Do all real numbers have a simple infinite continued fraction representation over the integer square roots?

Can an infinite continued fraction over the irrationals converge to an integer?

The monster continued fraction

Solving the continued fraction functional equation $f(x) = g(x) + \frac1{f(x^n)}$.

Does Khinchin's constant have an analog for nested radicals?

Numbers with "known" continued fractions

Continued fraction of the square $\sqrt{n}$ of the form $[a,\overline{k,b}]$

Convergence of partial quotients of $Q = \dfrac{1!}{1+\frac{2!}{\ddots}}$

Question about 12-tone musical scale and rational approximations

Why continued fraction gives initial solution of Pell's equation

Numbers whose decimal expansions are their own continued fractions.

Proposition about continued fractions

How we simplify the term $\frac{a^0}{2}+\frac{a^1}{2\cdot4}+\frac{a^2}{2\cdot4\cdot2}+\ldots+\frac{a^{n-1}+a^nx}{2\cdot4\cdot2\cdot4\ldots}$?

Proof of Binet's formula continued fraction

Explanation/Prove for this Continued fraction Algorithm

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