Question

Prove that if $x$ is a non-zero rational number, then $\tan(x)$ is not a rational number and use this to prove that $\pi$ is not a rational number.

score 2k · Answer 1 · 2013-01-26 12:59:15

2k

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Prove that if $x$ is a non-zero rational number, then $\tan(x)$ is not a rational number and use this to prove that $\pi$ is not a rational number.

Published on 26 Jan 2013 - 12:59

score 186 · Answer 2 · 2013-01-27 17:33:35

186

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Is there a power series representation for $\pi^{z}$, $z \in \mathbb{C}$?

Published on 27 Jan 2013 - 17:33

score 217 · Answer 3 · 2013-02-05 17:10:44

217

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Irrationality of $\pi$ from the spigot algorithm?

Published on 05 Feb 2013 - 17:10

score 265 · Answer 4 · 2013-02-07 12:38:27

265

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Get minimum N in approximation of pi

Published on 07 Feb 2013 - 12:38

score 13.4k · Answer 5 · 2013-02-10 02:13:15

13.4k

Views

Is sin(x) necessarily irrational where x is rational?

Published on 10 Feb 2013 - 2:13

score 3k · Answer 6 · 2013-02-14 03:22:36

3k

Views

Can an irrational number have a finite number of a certain digit?

Published on 14 Feb 2013 - 3:22

score 190 · Answer 7 · 2026-04-01 20:48:09

190

Views

Name for this problem regarding chords, and the area between two closed convex curves?

Published on 01 Apr 2026 - 20:48

score 3.9k · Answer 8 · 2013-02-22 13:27:03

3.9k

Views

What makes Pi special? What really makes it Irrational?

Published on 22 Feb 2013 - 13:27

score 2.1k · Answer 9 · 2013-02-24 18:20:17

2.1k

Views

How do I find the area of a circle inside a square?

Published on 24 Feb 2013 - 18:20

score 3.2k · Answer 10 · 2013-02-28 19:58:15

3.2k

Views

Intuitive explanation of Bailey-Borwein-Plouffe $\pi$ extraction formula?

Published on 28 Feb 2013 - 19:58

score 695 · Answer 11 · 2013-03-02 14:53:05

695

Views

Given $\tan x = 5/4$, where $\pi/4 < x < \pi$, use the trigonometric identities to find functions.

Published on 02 Mar 2013 - 14:53

score 640 · Answer 12 · 2013-03-06 07:44:46

640

Views

Why do some algorithms for computing pi converge faster?

Published on 06 Mar 2013 - 7:44

score 10.5k · Answer 13 · 2013-03-15 17:49:45

10.5k

Views

How to prove this identity $\pi=\sum\limits_{k=-\infty}^{\infty}\left(\frac{\sin(k)}{k}\right)^{2}\;$?

Published on 15 Mar 2013 - 17:49

score 551 · Answer 14 · 2026-03-26 11:18:17

551

Views

Understanding the Fundamental Theorem of Symmetric Polynomials within the context of proving $\pi$ transcendental

Published on 26 Mar 2026 - 11:18

score 45.9k · Answer 15 · 2013-03-22 04:09:16

45.9k

Views

A question comparing $\pi^e$ to $e^\pi$

Published on 22 Mar 2013 - 4:09

List Question

Prove that if $x$ is a non-zero rational number, then $\tan(x)$ is not a rational number and use this to prove that $\pi$ is not a rational number.

Is there a power series representation for $\pi^{z}$, $z \in \mathbb{C}$?

Irrationality of $\pi$ from the spigot algorithm?

Get minimum N in approximation of pi

Is sin(x) necessarily irrational where x is rational?

Can an irrational number have a finite number of a certain digit?

Name for this problem regarding chords, and the area between two closed convex curves?

What makes Pi special? What really makes it Irrational?

How do I find the area of a circle inside a square?

Intuitive explanation of Bailey-Borwein-Plouffe $\pi$ extraction formula?

Given $\tan x = 5/4$, where $\pi/4 < x < \pi$, use the trigonometric identities to find functions.

Why do some algorithms for computing pi converge faster?

How to prove this identity $\pi=\sum\limits_{k=-\infty}^{\infty}\left(\frac{\sin(k)}{k}\right)^{2}\;$?

Understanding the Fundamental Theorem of Symmetric Polynomials within the context of proving $\pi$ transcendental

A question comparing $\pi^e$ to $e^\pi$

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