List questions from triangle-inequality

Published on 23 Feb 2026 - 22:26

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Prove that if $\vec v$ and $\vec w$ are orthogonal then $\|\vec v+\vec w\|=\|\vec v\|+\|\vec w\|$

Published on 23 Feb 2026 - 22:28

66

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Why is $|x-y|^2 \geq \frac 12 |y|^2$ when $|x|$ is sufficiently small?

Published on 23 Feb 2026 - 22:30

33

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Is there some graphically way to (intuitive) understand the reverse triangle inequality in the $\ell^p$ spaces?

Published on 23 Feb 2026 - 22:29

1.3k

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Number of obtuse (or acute) triangles with sides $8$, $15$, and integer $x$

Published on 23 Feb 2026 - 22:28

220

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Is the "triangle inequality for reciprocals" a sufficient condition for altitudes of a triangle?

Published on 23 Feb 2026 - 22:30

245

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$L^1$ norm divided by $L^2$ norm: convexity

Published on 23 Feb 2026 - 22:27

229

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Ptolemy's inequality for Hilbert space

Published on 23 Feb 2026 - 22:27

40

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Proving an inequality absolute value

Published on 23 Feb 2026 - 22:25

425

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Generalized Triangle Inequality

Published on 11 Apr 2026 - 21:53

295

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Reverse Triangle Inequality inner product

Published on 23 Feb 2026 - 22:25

168

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Triangle inequality Bures distance

Published on 11 Apr 2026 - 11:24

107

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Does a continuous distance satisfy the triangle inequality?

Published on 10 Apr 2026 - 6:45

1k

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Is it possible to choose six triples of lengths from $1,2,3,\ldots, 20$ to form six triangles with equal perimeters?

Published on 11 Apr 2026 - 4:28

279

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Proving triangle inequality involving measures and symmetric differences

Published on 23 Feb 2026 - 22:27

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Showing $d$ is a metric

Prove that if $\vec v$ and $\vec w$ are orthogonal then $\|\vec v+\vec w\|=\|\vec v\|+\|\vec w\|$

Why is $|x-y|^2 \geq \frac 12 |y|^2$ when $|x|$ is sufficiently small?

Is there some graphically way to (intuitive) understand the reverse triangle inequality in the $\ell^p$ spaces?

Number of obtuse (or acute) triangles with sides $8$, $15$, and integer $x$

Is the "triangle inequality for reciprocals" a sufficient condition for altitudes of a triangle?

$L^1$ norm divided by $L^2$ norm: convexity

Ptolemy's inequality for Hilbert space

Proving an inequality absolute value

Generalized Triangle Inequality

Reverse Triangle Inequality inner product

Triangle inequality Bures distance

Does a continuous distance satisfy the triangle inequality?

Is it possible to choose six triples of lengths from $1,2,3,\ldots, 20$ to form six triangles with equal perimeters?

Proving triangle inequality involving measures and symmetric differences

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