Question

Generalizing how well an arbitrary set approximates a number?

score 60 · Answer 1 · 2026-02-23 19:15:19

60

Views

Generalizing how well an arbitrary set approximates a number?

Published on 23 Feb 2026 - 19:15

score 170 · Answer 2 · 2022-03-12 18:17:22

170

Views

Is there a number such that the sequence of its best rational approximations is strictly increasing?

Published on 12 Mar 2022 - 18:17

score 340 · Answer 3 · 2022-03-20 04:02:12

340

Views

Relationship between Dirichlet's Approximation Theorem and Convergents

Published on 20 Mar 2022 - 4:02

score 399 · Answer 4 · 2022-03-21 11:42:48

399

Views

Upper and lower bounds for $n|\sin(n)|$

Published on 21 Mar 2022 - 11:42

score 81 · Answer 5 · 2022-03-26 11:23:34

81

Views

Difficulty with diophantine approximation: building sets with arbitrary lower and upper natural densities

Published on 26 Mar 2022 - 11:23

score 82 · Answer 6 · 2022-03-31 13:25:08

82

Views

Is the convergence of these two series equivalent? (They come from Khinchin's theorem and the Duffin-Schaeffer conjecture.)

Published on 31 Mar 2022 - 13:25

score 85 · Answer 7 · 2022-04-20 00:20:49

85

Views

Why is $|dx-c|<|qx-p|$ the condition for the best rational approximations of the second kind

Published on 20 Apr 2022 - 0:20

score 60 · Answer 8 · 2022-04-25 16:01:14

60

Views

lonely runner conjecture for 3 runners

Published on 25 Apr 2022 - 16:01

score 52 · Answer 9 · 2022-04-26 01:11:10

52

Views

Lagrange's best approximations law proof by contradiction doubt

Published on 26 Apr 2022 - 1:11

score 43 · Answer 10 · 2022-04-27 19:14:38

43

Views

Range of Lagrange's 'best approximations' law

Published on 27 Apr 2022 - 19:14

score 80 · Answer 11 · 2022-05-02 06:15:39

80

Views

Does every line through the origin come arbitrarily close to some other lattice point?

Published on 02 May 2022 - 6:15

score 73 · Answer 12 · 2022-05-03 20:33:24

73

Views

Rational solutions of the equation $2xy^2=kx^2+1$

Published on 03 May 2022 - 20:33

score 27 · Answer 13 · 2022-05-08 18:15:18

27

Views

Validity of Equality in the Condition for a Rational to be a Convergent

Published on 08 May 2022 - 18:15

score 217 · Answer 14 · 2022-05-08 22:12:30

217

Views

If $\Big|x-\frac{p}{q}\Big|<\frac{1}{2q^2}$ then $p/q$ is necessarily one of the convergents : Extend the proof to irrational $x$

Published on 08 May 2022 - 22:12

score 90 · Answer 15 · 2022-05-13 21:30:00

90

Views

Does $\lfloor \tan (n)\rfloor =n$ have infinite roots?

Published on 13 May 2022 - 21:30

List Question

Generalizing how well an arbitrary set approximates a number?

Is there a number such that the sequence of its best rational approximations is strictly increasing?

Relationship between Dirichlet's Approximation Theorem and Convergents

Upper and lower bounds for $n|\sin(n)|$

Difficulty with diophantine approximation: building sets with arbitrary lower and upper natural densities

Is the convergence of these two series equivalent? (They come from Khinchin's theorem and the Duffin-Schaeffer conjecture.)

Why is $|dx-c|<|qx-p|$ the condition for the best rational approximations of the second kind

lonely runner conjecture for 3 runners

Lagrange's best approximations law proof by contradiction doubt

Range of Lagrange's 'best approximations' law

Does every line through the origin come arbitrarily close to some other lattice point?

Rational solutions of the equation $2xy^2=kx^2+1$

Validity of Equality in the Condition for a Rational to be a Convergent

If $\Big|x-\frac{p}{q}\Big|<\frac{1}{2q^2}$ then $p/q$ is necessarily one of the convergents : Extend the proof to irrational $x$

Does $\lfloor \tan (n)\rfloor =n$ have infinite roots?

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