List questions from triangle-inequality

Published on 25 Feb 2023 - 13:01

35

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Is there any simple way of proving triangle inequality for $d(x,y)= \dfrac{2|x-y|}{\sqrt{1+x^2}+\sqrt{1+y^2}}, \,\,x,y\in \mathbb{R}$

Published on 03 Mar 2023 - 15:45

109

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How many triangles can be formed so that the area of $\triangle ABC$ is 9 times $\triangle DEF$?

Published on 05 Mar 2023 - 17:41

40

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Lemma for the Bescicovitch covering lemma

Published on 07 Mar 2023 - 22:42

96

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Triangle Inequality for this metric

Published on 09 Mar 2023 - 21:59

44

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How to prove the triangle inequality in the case of an n-sided polygon?

Published on 23 Mar 2023 - 3:28

78

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Alternative triangle inequality proof for complex numbers

Published on 30 Mar 2023 - 22:54

158

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Does angle between vectors satisfy triangle inequality?

Published on 31 Mar 2023 - 22:55

81

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Does the reverse triangle inequality holds for Wasserstein-1 distance?

Published on 04 Apr 2023 - 22:49

100

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proof of $\|a+b\|_2\le\|a\|_2+\|b\|_2$

Published on 11 Apr 2023 - 3:52

37

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Unclear passage in this triangle inequality $\cup$ Cauchy-Schwarz proof

Published on 17 Apr 2023 - 13:18

244

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Simrank distance triangle inequality

Published on 04 May 2023 - 20:53

37

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Simple inequality using density of rationals

Published on 27 May 2023 - 22:41

109

Views

Case of equality in spectral norm matrix triangle inequality

Published on 30 May 2023 - 9:36

123

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Prove that a triangle exists using the triangle inequality.

Published on 08 Jun 2023 - 13:11

List Question

Proving that $\lVert x\rVert=\sqrt{\langle x,x \rangle}$ is a norm (triangle inequality).

Is there any simple way of proving triangle inequality for $d(x,y)= \dfrac{2|x-y|}{\sqrt{1+x^2}+\sqrt{1+y^2}}, \,\,x,y\in \mathbb{R}$

How many triangles can be formed so that the area of $\triangle ABC$ is 9 times $\triangle DEF$?

Lemma for the Bescicovitch covering lemma

Triangle Inequality for this metric

How to prove the triangle inequality in the case of an n-sided polygon?

Alternative triangle inequality proof for complex numbers

Does angle between vectors satisfy triangle inequality?

Does the reverse triangle inequality holds for Wasserstein-1 distance?

proof of $\|a+b\|_2\le\|a\|_2+\|b\|_2$

Unclear passage in this triangle inequality $\cup$ Cauchy-Schwarz proof

Simrank distance triangle inequality

Simple inequality using density of rationals

Case of equality in spectral norm matrix triangle inequality

Prove that a triangle exists using the triangle inequality.

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