Question

Recent progress in the irrationality measure of $\pi$

score 1.3k · Answer 1 · 2026-02-23 00:49:06

1.3k

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Recent progress in the irrationality measure of $\pi$

Published on 23 Feb 2026 - 0:49

score 1.3k · Answer 2 · 2026-02-23 00:49:07

1.3k

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Can multiples of two reals stay separated?

Published on 23 Feb 2026 - 0:49

score 103 · Answer 3 · 2026-02-23 00:48:14

103

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The irrational of such constant

Published on 23 Feb 2026 - 0:48

score 51 · Answer 4 · 2026-02-23 00:46:09

51

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Silly question about irrationally measure

Published on 23 Feb 2026 - 0:46

score 45 · Answer 5 · 2026-02-23 00:49:33

45

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Can we make the definition of irrationality measure ‘stronger’?

Published on 23 Feb 2026 - 0:49

score 1.1k · Answer 6 · 2026-02-22 22:54:18

1.1k

Views

Are all transcendental numbers a zero of a power series?

Published on 22 Feb 2026 - 22:54

score 552 · Answer 7 · 2026-02-23 00:51:11

552

Views

Why can we not establish the irrationality of Catalan's constant the same way as $\zeta(3)$?

Published on 23 Feb 2026 - 0:51

score 56 · Answer 8 · 2026-02-23 00:50:35

56

Views

If two real numbers are immesurable can an integer sum between the two get as close to any real number as we like?

Published on 23 Feb 2026 - 0:50

score 140 · Answer 9 · 2026-02-23 00:47:56

140

Views

Prove that irrationality measure is never less than 1

Published on 23 Feb 2026 - 0:47

score 185 · Answer 10 · 2026-02-23 00:49:32

185

Views

Does $\sum_{k=1}^n|\cot \sqrt2\pi k|$ tends to $An\ln n$ as $n\to\infty$?

Published on 23 Feb 2026 - 0:49

score 265 · Answer 11 · 2026-02-23 00:51:18

265

Views

Can the formula $\frac\pi2=(\frac21)^{1/2}(\frac{2^2}{1\cdot3})^{1/4}(\frac{2^3\cdot4}{1\cdot3^3})^{1/8}\cdots$ prove the irrationality of $\pi$?

Published on 23 Feb 2026 - 0:51

score 106 · Answer 12 · 2026-02-23 02:20:27

106

Views

Irrationality measure of a polynomial in $\pi$

Published on 23 Feb 2026 - 2:20

score 512 · Answer 13 · 2026-02-23 02:21:51

512

Views

Applying the Beukers-like irrationality proof for $\zeta(2)$ and $\zeta(3)$ to Catalan's constant: where does it fail?

Published on 23 Feb 2026 - 2:21

score 145 · Answer 14 · 2026-02-23 02:17:48

145

Views

Do there exist numbers with non-integer irrationality measure?

Published on 23 Feb 2026 - 2:17

score 130 · Answer 15 · 2026-02-23 02:21:50

130

Views

What about irrationality of $a_n=(1-\frac12)^{(\frac12-\frac13)^{...^{(\frac{1}{n}-\frac{1}{n+1})}}}$?

Published on 23 Feb 2026 - 2:21

List Question

Recent progress in the irrationality measure of $\pi$

Can multiples of two reals stay separated?

The irrational of such constant

Silly question about irrationally measure

Can we make the definition of irrationality measure ‘stronger’?

Are all transcendental numbers a zero of a power series?

Why can we not establish the irrationality of Catalan's constant the same way as $\zeta(3)$?

If two real numbers are immesurable can an integer sum between the two get as close to any real number as we like?

Prove that irrationality measure is never less than 1

Does $\sum_{k=1}^n|\cot \sqrt2\pi k|$ tends to $An\ln n$ as $n\to\infty$?

Can the formula $\frac\pi2=(\frac21)^{1/2}(\frac{2^2}{1\cdot3})^{1/4}(\frac{2^3\cdot4}{1\cdot3^3})^{1/8}\cdots$ prove the irrationality of $\pi$?

Irrationality measure of a polynomial in $\pi$

Applying the Beukers-like irrationality proof for $\zeta(2)$ and $\zeta(3)$ to Catalan's constant: where does it fail?

Do there exist numbers with non-integer irrationality measure?

What about irrationality of $a_n=(1-\frac12)^{(\frac12-\frac13)^{...^{(\frac{1}{n}-\frac{1}{n+1})}}}$?

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