Question

How can I get the Pythagorean theorem from triangle inequality?

score 241 · Answer 1 · 2026-02-23 01:03:57

241

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How can I get the Pythagorean theorem from triangle inequality?

Published on 23 Feb 2026 - 1:03

score 129 · Answer 2 · 2026-02-23 01:04:10

129

Views

Probability of forming a triangle from a unit line segment with two random cuts

Published on 23 Feb 2026 - 1:04

score 41 · Answer 3 · 2026-02-23 01:08:26

41

Views

Showing $|f(x)| > \frac{1}{2} |f(p)|$ if f continous and $f(p)$ not $0$

Published on 23 Feb 2026 - 1:08

score 35 · Answer 4 · 2026-02-23 01:05:32

35

Views

Did I make a mistake in my proof of triangular ineqality by squaring both sides?

Published on 23 Feb 2026 - 1:05

score 94 · Answer 5 · 2026-04-05 11:02:25

94

Views

Prove a metric space

Published on 05 Apr 2026 - 11:02

score 146 · Answer 6 · 2026-02-23 01:02:47

146

Views

A problem regarding the in-equality of complex numbers .

Published on 23 Feb 2026 - 1:02

score 1.2k · Answer 7 · 2026-02-23 01:06:12

1.2k

Views

Is this a valid proof for the reverse triangle inequality: Given $x,\,y\in\mathbb{R}^n$, $\|x-y\|\ge |\|x\| - \|y\||$.

Published on 23 Feb 2026 - 1:06

score 73 · Answer 8 · 2026-03-22 14:02:44

73

Views

$|a\alpha-b\beta|\leq|a-b|+|\alpha-\beta|$

Published on 22 Mar 2026 - 14:02

score 162 · Answer 9 · 2026-02-23 01:07:06

162

Views

Is it possible to prove the triangle inequality in inner product spaces without using the Cauchy-Schwartz inequality?

Published on 23 Feb 2026 - 1:07

score 33 · Answer 10 · 2026-03-22 18:14:54

33

Views

Change of angle given a load (geometric problem)

Published on 22 Mar 2026 - 18:14

score 81 · Answer 11 · 2026-02-23 01:05:33

81

Views

Can someone prove the triangle inequality for the following $d$?

Published on 23 Feb 2026 - 1:05

score 61 · Answer 12 · 2026-02-23 01:03:00

61

Views

Show that the angle function between two points on the unit circle satisfies the triangle inequality

Published on 23 Feb 2026 - 1:03

score 49 · Answer 13 · 2026-02-23 01:07:34

49

Views

Proving $ \mid a - x| > |b - x|$ implies $(a - b)\cdot(x-b)<0$ where $a,b,x\in\mathbb{R}^N$

Published on 23 Feb 2026 - 1:07

score 117 · Answer 14 · 2026-02-23 01:04:08

117

Views

Proof that 2-norm is norm on $\mathbb{R}^2$ without C.S. inequality

Published on 23 Feb 2026 - 1:04

score 367 · Answer 15 · 2026-02-23 01:08:26

367

Views

Show that if equality takes place in triangle inequality then one of the vectors is either null vector or they are linearly dependent

Published on 23 Feb 2026 - 1:08

List Question

How can I get the Pythagorean theorem from triangle inequality?

Probability of forming a triangle from a unit line segment with two random cuts

Showing $|f(x)| > \frac{1}{2} |f(p)|$ if f continous and $f(p)$ not $0$

Did I make a mistake in my proof of triangular ineqality by squaring both sides?

Prove a metric space

A problem regarding the in-equality of complex numbers .

Is this a valid proof for the reverse triangle inequality: Given $x,\,y\in\mathbb{R}^n$, $\|x-y\|\ge |\|x\| - \|y\||$.

$|a\alpha-b\beta|\leq|a-b|+|\alpha-\beta|$

Is it possible to prove the triangle inequality in inner product spaces without using the Cauchy-Schwartz inequality?

Change of angle given a load (geometric problem)

Can someone prove the triangle inequality for the following $d$?

Show that the angle function between two points on the unit circle satisfies the triangle inequality

Proving $ \mid a - x| > |b - x|$ implies $(a - b)\cdot(x-b)<0$ where $a,b,x\in\mathbb{R}^N$

Proof that 2-norm is norm on $\mathbb{R}^2$ without C.S. inequality

Show that if equality takes place in triangle inequality then one of the vectors is either null vector or they are linearly dependent

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