Question

Does there exist an irrational number $x$ such that both $x^π$ and $π^x$ are also irrational?

score 107 · Answer 1 · 2024-03-05 03:50:20

107

Views

Does there exist an irrational number $x$ such that both $x^π$ and $π^x$ are also irrational?

Published on 05 Mar 2024 - 3:50

score 37 · Answer 2 · 2026-03-27 07:48:18

37

Views

Parametric representation of the Euler-Beta function, Zeta functions and pi

Published on 27 Mar 2026 - 7:48

score 83 · Answer 3 · 2026-03-27 05:41:58

83

Views

How to calculate the ratio of convergence for Euler's, Gauss' and Viète's approximation of $\pi$?

Published on 27 Mar 2026 - 5:41

score 105 · Answer 4 · 2026-03-25 13:58:01

105

Views

Might there be an $n^{\text{th}}$ digit of $\pi$ where the sequence becomes palindromic?

Published on 25 Mar 2026 - 13:58

score 108 · Answer 5 · 2024-03-23 07:23:10

108

Views

Why no one uses the product formula for sine function to calculate $\pi$?

Published on 23 Mar 2024 - 7:23

score 42 · Answer 6 · 2026-03-27 23:19:59

42

Views

Approximation of $\pi$ step by step by using $\sin\frac{60}{2^x}(3(2^x))=\pi$

Published on 27 Mar 2026 - 23:19

score 126 · Answer 7 · 2024-03-30 13:42:38

126

Views

A new formula for $\pi$ using cheated Bernstein's polynomials with composition and Gamma function?

Published on 30 Mar 2024 - 13:42

score 736 · Answer 8 · 2026-03-28 02:23:45

736

Views

"Bizarre" continued fraction of Ramanujan! But where's the proof?

Published on 28 Mar 2026 - 2:23

score 2.1k · Answer 9 · 2026-03-26 13:01:18

2.1k

Views

How was this approximation of $\pi$ involving $\sqrt{5}$ arrived at?

Published on 26 Mar 2026 - 13:01

score 1.5k · Answer 10 · 2015-01-05 20:27:31

1.5k

Views

$e^{\pi\sqrt N}$ is very close to an integer for some smallish $N$s. What about $\pi^{e\sqrt N}$?

Published on 05 Jan 2015 - 20:27

score 3.4k · Answer 11 · 2026-03-26 09:41:00

3.4k

Views

Proof that at most one of $e\pi$ and $e+\pi$ can be rational

Published on 26 Mar 2026 - 9:41

score 116 · Answer 12 · 2015-01-09 12:47:11

116

Views

How to show$\frac{\pi}{4} = \frac{2\cdot4\cdot4\cdot6\cdot6\cdot8 \dotsm}{3\cdot3\cdot5\cdot5\cdot7\cdot7 \dotsm}$?

Published on 09 Jan 2015 - 12:47

score 497 · Answer 13 · 2015-01-09 13:24:48

497

Views

Rational approximation of pi

Published on 09 Jan 2015 - 13:24

score 452 · Answer 14 · 2015-01-11 19:38:38

452

Views

How can I improve my explanation of why the ratio $\pi=\frac{C}{d}$ holds for all circles?

Published on 11 Jan 2015 - 19:38

score 428 · Answer 15 · 2015-01-13 18:07:01

428

Views

Which is greater $e^{\pi}$ or $\pi^e$?

Published on 13 Jan 2015 - 18:07

List Question

Does there exist an irrational number $x$ such that both $x^π$ and $π^x$ are also irrational?

Parametric representation of the Euler-Beta function, Zeta functions and pi

How to calculate the ratio of convergence for Euler's, Gauss' and Viète's approximation of $\pi$?

Might there be an $n^{\text{th}}$ digit of $\pi$ where the sequence becomes palindromic?

Why no one uses the product formula for sine function to calculate $\pi$?

Approximation of $\pi$ step by step by using $\sin\frac{60}{2^x}(3(2^x))=\pi$

A new formula for $\pi$ using cheated Bernstein's polynomials with composition and Gamma function?

"Bizarre" continued fraction of Ramanujan! But where's the proof?

How was this approximation of $\pi$ involving $\sqrt{5}$ arrived at?

$e^{\pi\sqrt N}$ is very close to an integer for some smallish $N$s. What about $\pi^{e\sqrt N}$?

Proof that at most one of $e\pi$ and $e+\pi$ can be rational

How to show$\frac{\pi}{4} = \frac{2\cdot4\cdot4\cdot6\cdot6\cdot8 \dotsm}{3\cdot3\cdot5\cdot5\cdot7\cdot7 \dotsm}$?

Rational approximation of pi

How can I improve my explanation of why the ratio $\pi=\frac{C}{d}$ holds for all circles?

Which is greater $e^{\pi}$ or $\pi^e$?

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