Phrase guide

Euclidean space

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

Ordinary n-dimensional space, characterized by an infinite extent along each dimension and a constant distance between any pair of parallel lines.

Definition source: English Wiktionary via Wiktextract

Usage: countable, uncountable

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

noun

Meaning 2

Any real vector space on which a real-valued inner product (and, consequently, a metric) is defined.

Definition source: English Wiktionary via Wiktextract

Usage: countable, uncountable

Topics: mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

3

noun

Meaning 3

a space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional

Definition source: Princeton WordNet 3.0

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

Broader terms: metric space

History

Etymology

No etymology was provided for this word.

Across languages

Translations

19 source translations are retained for this English entry.

  • Czech: euklidovský prostor — ordinary space
  • Danish: euklidisk rum — ordinary space
  • Finnish: euklidinen avaruus — ordinary space
  • French: espace euclidien — ordinary space
  • Greek: Ευκλείδειος χώρος (Efkleídeios chóros) — ordinary space
  • Hungarian: euklideszi tér — ordinary space
  • Japanese: ユークリッド空間 (Yūkuriddo kūkan) — ordinary space
  • Korean: 유클리드 공간 (yukeullideu gonggan) — ordinary space
  • Polish: przestrzeń euklidesowa — ordinary space
  • Portuguese: espaço euclidiano — ordinary space
  • Romanian: spațiu euclidian — ordinary space
  • Russian: евкли́дово простра́нство (jevklídovo prostránstvo) — ordinary space
  • Serbo-Croatian: euklidski prostor — ordinary space
  • Spanish: espacio euclídeo — ordinary space
  • Spanish: espacio euclidiano — ordinary space
  • Swedish: euklidiskt rum — ordinary space
  • Thai: ปริภูมิแบบยุคลิด — ordinary space
  • Korean: 유클리드 공간 (yukeullideu gonggan) — type of vector space
  • Polish: przestrzeń euklidesowa — type of vector space