triangle inequality

noun

The inequality that states that the magnitude of the sum of two vectors is less than or equal to the sum of the magnitudes of the vectors.

“d(x,z)≤d(x,y)+d(y,z)”

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Meanings

nountriangle inequality (plural triangle inequalities)

plural triangle inequalities

  1. mathematical analysisThe inequality that states that the magnitude of the sum of two vectors is less than or equal to the sum of the magnitudes of the vectors.

    ‖ mathbf x+ mathbf y‖≤‖ mathbf x‖+‖ mathbf y‖

  2. mathematical analysisThe inequality that states that the distance between two points is less than or equal to the sum of the distances between the first two points and some third point.

    d(x,z)≤d(x,y)+d(y,z)

  3. by abstractionmathematical analysisEither of the above two inequalities, considered as one of the axioms which a function must satisfy to be a norm or metric respectively.

Translations

Chinese 三角不等式
  • 三角不等式 (sānjiǎo bùděngshì)the triangle inequality
Dutch driehoeksongelijkheid
  • driehoeksongelijkheidthe triangle inequality
Finnish kolmioepäyhtälö
  • kolmioepäyhtälöthe triangle inequality
French inégalité triangulaire
  • inégalité triangulairethe triangle inequality
German Dreiecksungleichung
  • Dreiecksungleichungthe triangle inequality
Hebrew אי שוויון המשולש
  • אי שוויון המשולשthe triangle inequality
Italian disuguaglianza triangolare
  • disuguaglianza triangolarethe triangle inequality
Japanese 三角不等式
  • 三角不等式 (sankaku futōshiki)the triangle inequality
Polish nierówność trójkąta
  • nierówność trójkątathe triangle inequality
Portuguese desigualdade triangular
  • desigualdade triangularthe triangle inequality
Romanian inegalitatea triunghiului
  • inegalitatea triunghiuluithe triangle inequality
Russian нера́венство треуго́льника
  • нера́венство треуго́льника (nerávenstvo treugólʹnika)the triangle inequality
Spanish desigualdad del triángulo
  • desigualdad del triángulothe triangle inequality
Swedish triangelolikhet
  • triangelolikhetthe triangle inequality
Cite this entry
APA

triangle inequality. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/triangle%20inequality

MLA

“triangle inequality.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/triangle%20inequality. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “triangle inequality,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/triangle%20inequality.

Source: triangle inequality on Wiktionary, CC BY-SA 4.0.