List questions from transcendental-numbers

Published on 18 Apr 2013 - 4:16

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Why is the concept of transcendental numbers linked with rational coefficients? Why not real nor complex coefficients?

Published on 18 Apr 2013 - 9:36

727

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Proving that $\frac{\pi}{2}=\prod_{k=2}^{\infty}\left(1+\frac{(-1)^{(p_{k}-1)/2}}{p_{k}} \right )^{-1}$ an identity of Euler's.

Published on 25 Apr 2013 - 16:40

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Is the positive root of the equation $x^{x^x}=2$, $x=1.47668433...$ a transcendental number?

Published on 26 Mar 2026 - 3:13

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Irrational numbers, decimal representation

Published on 26 Mar 2026 - 3:10

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What is the role of mathematical intuition and common sense in questions of irrationality or transcendence of values of special functions?

Published on 09 May 2013 - 2:52

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What are examples of unexpected algebraic numbers of high degree occured in some math problems?

Published on 09 May 2013 - 22:39

212

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The Tribonacci constant and the Dragon

Published on 14 May 2013 - 17:14

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Can a finitely generated $\mathbb{Z}$-algebra contain $\mathbb{Q}$?

Published on 23 May 2013 - 16:02

304

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The set $\{\frac{3^m}{\alpha^n}:\;m,n\in\mathbb Z\}$ is dense in $\mathbb R_+$

Published on 20 Jun 2013 - 3:15

762

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Numbers with no finite representation on paper

Published on 26 Jun 2013 - 20:04

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Can $x^{x^{x^x}}$ be a rational number?

Published on 26 Mar 2026 - 14:29

382

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Why does this function generate pretty randomish numbers?

Published on 26 Mar 2026 - 6:17

196

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Transcendental proofs vs. Irrational proofs

Published on 25 Jul 2013 - 4:12

313

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$\pi$ and $\ln4$ relations. Even and Odd alternating sums.

Published on 26 Jul 2013 - 2:59

List Question

Non-existence of irrational numbers?

Why is the concept of transcendental numbers linked with rational coefficients? Why not real nor complex coefficients?

Proving that $\frac{\pi}{2}=\prod_{k=2}^{\infty}\left(1+\frac{(-1)^{(p_{k}-1)/2}}{p_{k}} \right )^{-1}$ an identity of Euler's.

Is the positive root of the equation $x^{x^x}=2$, $x=1.47668433...$ a transcendental number?

Irrational numbers, decimal representation

What is the role of mathematical intuition and common sense in questions of irrationality or transcendence of values of special functions?

What are examples of unexpected algebraic numbers of high degree occured in some math problems?

The Tribonacci constant and the Dragon

Can a finitely generated $\mathbb{Z}$-algebra contain $\mathbb{Q}$?

The set $\{\frac{3^m}{\alpha^n}:\;m,n\in\mathbb Z\}$ is dense in $\mathbb R_+$

Numbers with no finite representation on paper

Can $x^{x^{x^x}}$ be a rational number?

Why does this function generate pretty randomish numbers?

Transcendental proofs vs. Irrational proofs

$\pi$ and $\ln4$ relations. Even and Odd alternating sums.

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