Question

Inequality related to the continued fraction expansion of $\sqrt 3$

score 281 · Answer 1 · 2013-08-19 19:36:10

281

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Inequality related to the continued fraction expansion of $\sqrt 3$

Published on 19 Aug 2013 - 19:36

score 203 · Answer 2 · 2013-08-24 07:54:30

203

Views

After $n$ iterations of the continued fraction algorithm, what kind of rational numbers will have terminated?

Published on 24 Aug 2013 - 7:54

score 752 · Answer 3 · 2013-09-03 15:39:27

752

Views

Continued fraction with prime reciprocal entries

Published on 03 Sep 2013 - 15:39

score 62 · Answer 4 · 2013-09-04 21:34:31

62

Views

What is the rate of decay of $\min\{k\xi-\lfloor k\xi\rfloor|k\in\{1,\dots,n\}\}$, for irrational $\xi$?

Published on 04 Sep 2013 - 21:34

score 8.7k · Answer 5 · 2013-09-05 05:41:02

8.7k

Views

Computing Infinite Continued Fractions

Published on 05 Sep 2013 - 5:41

score 518 · Answer 6 · 2013-09-15 18:27:23

518

Views

Evaluation of Rogers-Ramanujan continued fraction $R(e^{-2\pi/5})$

Published on 15 Sep 2013 - 18:27

score 146 · Answer 7 · 2013-09-23 08:56:38

146

Views

Does the continued fractions $3+\frac{1}{5+\frac{1}{7+\cdots}}$ equal $\pi$?

Published on 23 Sep 2013 - 8:56

score 57 · Answer 8 · 2013-09-25 04:34:46

57

Views

Convergence of a sequence to a value and not another.

Published on 25 Sep 2013 - 4:34

score 2.4k · Answer 9 · 2013-09-28 21:07:18

2.4k

Views

A strange "pattern" in the continued fraction convergents of pi?

Published on 28 Sep 2013 - 21:07

score 178 · Answer 10 · 2013-09-29 00:48:11

178

Views

Why does this pattern fail (sometimes) for the continued fraction convergents of $\sqrt{2}$?

Published on 29 Sep 2013 - 0:48

score 240 · Answer 11 · 2013-10-01 10:28:24

240

Views

Can the number of digits in the denominator of a node in Stern-Brocot-Tree decrease in its children?

Published on 01 Oct 2013 - 10:28

score 562 · Answer 12 · 2013-10-02 10:22:41

562

Views

How long should you descent in Stern-Brocot-Tree to get a fixed approximation guarantee?

Published on 02 Oct 2013 - 10:22

score 233 · Answer 13 · 2013-10-03 03:44:40

233

Views

Are continued fractions a mere curiosity?

Published on 03 Oct 2013 - 3:44

score 167 · Answer 14 · 2013-10-05 23:26:00

167

Views

Is the infinite continued fraction $[0;0,0,\ldots]=0$?

Published on 05 Oct 2013 - 23:26

score 1k · Answer 15 · 2013-10-06 09:29:06

1k

Views

About continued fractions as best rational approximations

Published on 06 Oct 2013 - 9:29

List Question

Inequality related to the continued fraction expansion of $\sqrt 3$

After $n$ iterations of the continued fraction algorithm, what kind of rational numbers will have terminated?

Continued fraction with prime reciprocal entries

What is the rate of decay of $\min\{k\xi-\lfloor k\xi\rfloor|k\in\{1,\dots,n\}\}$, for irrational $\xi$?

Computing Infinite Continued Fractions

Evaluation of Rogers-Ramanujan continued fraction $R(e^{-2\pi/5})$

Does the continued fractions $3+\frac{1}{5+\frac{1}{7+\cdots}}$ equal $\pi$?

Convergence of a sequence to a value and not another.

A strange "pattern" in the continued fraction convergents of pi?

Why does this pattern fail (sometimes) for the continued fraction convergents of $\sqrt{2}$?

Can the number of digits in the denominator of a node in Stern-Brocot-Tree decrease in its children?

How long should you descent in Stern-Brocot-Tree to get a fixed approximation guarantee?

Are continued fractions a mere curiosity?

Is the infinite continued fraction $[0;0,0,\ldots]=0$?

About continued fractions as best rational approximations

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