Phrase guide

triangle inequality

noun · 3 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

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.

Definition source: English Wiktionary via Wiktextract

Topics: mathematical-analysis, mathematics, sciences

Examples

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

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

noun

Meaning 2

The 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.

Definition source: English Wiktionary via Wiktextract

Topics: mathematical-analysis, mathematics, sciences

Examples

  • d(x,z)≤d(x,y)+d(y,z)

Meaning relationships

Synonyms: none provided

Antonyms: none provided

3

noun

Meaning 3

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

Definition source: English Wiktionary via Wiktextract

Qualifier: by abstraction

Topics: mathematical-analysis, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.

Across languages

Translations

14 source translations are retained for this English entry.

  • Chinese: 三角不等式 (sānjiǎo bùděngshì) — the triangle inequality
  • Dutch: driehoeksongelijkheid — the triangle inequality
  • Finnish: kolmioepäyhtälö — the triangle inequality
  • French: inégalité triangulaire — the triangle inequality
  • German: Dreiecksungleichung — the triangle inequality
  • Hebrew: אי שוויון המשולש — the triangle inequality
  • Italian: disuguaglianza triangolare — the triangle inequality
  • Japanese: 三角不等式 (sankaku futōshiki) — the triangle inequality
  • Polish: nierówność trójkąta — the triangle inequality
  • Portuguese: desigualdade triangular — the triangle inequality
  • Romanian: inegalitatea triunghiului — the triangle inequality
  • Russian: нера́венство треуго́льника (nerávenstvo treugólʹnika) — the triangle inequality
  • Spanish: desigualdad del triángulo — the triangle inequality
  • Swedish: triangelolikhet — the triangle inequality