Question

How to prove $\mathbb{Q}(\pi)$ and $\mathbb{Q}(e)$ are not the same field?

score 640 · Answer 1 · 2026-03-28 19:39:56

640

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How to prove $\mathbb{Q}(\pi)$ and $\mathbb{Q}(e)$ are not the same field?

Published on 28 Mar 2026 - 19:39

score 553 · Answer 2 · 2017-09-08 15:44:36

553

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Intuition why a combined inscribed and circumscribed polygon converge faster to $\pi$?

Published on 08 Sep 2017 - 15:44

score 208 · Answer 3 · 2017-09-10 06:43:12

208

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Limit points of a sequence constructed from pi (if pi is normal)

Published on 10 Sep 2017 - 6:43

score 91 · Answer 4 · 2017-09-15 17:23:36

91

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Proving that if $a,b \in \mathbb{N}^*$ then $\frac{\pi a^n}{n!} \int ^{1}_{0}x^n(1-x)^n \sin (\pi x) dx \in \mathbb{N}$

Published on 15 Sep 2017 - 17:23

score 187 · Answer 5 · 2017-09-18 18:14:31

187

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Variance of first n binary digits of pi?

Published on 18 Sep 2017 - 18:14

score 347 · Answer 6 · 2026-03-25 12:55:24

347

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Prove that ${e\over {\pi}}\lt{\sqrt3\over{2}}$ without using a calculator.

Published on 25 Mar 2026 - 12:55

score 260 · Answer 7 · 2017-09-24 13:23:35

260

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$\pi$ as a product of a fraction and $\sqrt2$

Published on 24 Sep 2017 - 13:23

score 54 · Answer 8 · 2026-03-30 00:19:24

54

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Nine isosceles triangles whose angles give a fixed integer both with sine and cosine.

Published on 30 Mar 2026 - 0:19

score 253 · Answer 9 · 2017-09-29 10:51:40

253

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Geometry: Circumference of circle without $\pi$

Published on 29 Sep 2017 - 10:51

score 52 · Answer 10 · 2017-10-11 03:19:07

52

Views

Prove product of sequence less than other for all n using induction

Published on 11 Oct 2017 - 3:19

score 198 · Answer 11 · 2017-10-12 16:42:56

198

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Does pi have any combination of two numbers that the distance between them equal some natural number

Published on 12 Oct 2017 - 16:42

score 511 · Answer 12 · 2026-03-26 18:56:32

511

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Prove that ${e\over {\pi}}\lt{1\over {2\gamma}}$ without using a calculator.

Published on 26 Mar 2026 - 18:56

score 177 · Answer 13 · 2017-10-15 04:29:10

177

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Why are there so few 7s in the first thousand digits of pi?

Published on 15 Oct 2017 - 4:29

score 65 · Answer 14 · 2017-10-17 05:50:02

65

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Some alternating series converging to values relating to $\pi$.

Published on 17 Oct 2017 - 5:50

score 5.4k · Answer 15 · 2017-10-23 06:45:38

5.4k

Views

Simplest way to get the lower bound $\pi > 3.14$

Published on 23 Oct 2017 - 6:45

List Question

How to prove $\mathbb{Q}(\pi)$ and $\mathbb{Q}(e)$ are not the same field?

Intuition why a combined inscribed and circumscribed polygon converge faster to $\pi$?

Limit points of a sequence constructed from pi (if pi is normal)

Proving that if $a,b \in \mathbb{N}^*$ then $\frac{\pi a^n}{n!} \int ^{1}_{0}x^n(1-x)^n \sin (\pi x) dx \in \mathbb{N}$

Variance of first n binary digits of pi?

Prove that ${e\over {\pi}}\lt{\sqrt3\over{2}}$ without using a calculator.

$\pi$ as a product of a fraction and $\sqrt2$

Nine isosceles triangles whose angles give a fixed integer both with sine and cosine.

Geometry: Circumference of circle without $\pi$

Prove product of sequence less than other for all n using induction

Does pi have any combination of two numbers that the distance between them equal some natural number

Prove that ${e\over {\pi}}\lt{1\over {2\gamma}}$ without using a calculator.

Why are there so few 7s in the first thousand digits of pi?

Some alternating series converging to values relating to $\pi$.

Simplest way to get the lower bound $\pi > 3.14$

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