Euclidean space

English

Alternative forms

• Euclidian space

Noun

Euclidean space (countable and uncountable, plural Euclidean spaces)

1. Ordinary two- or three-dimensional space, characterised by an infinite extent along each dimension and a constant distance between any pair of parallel lines.
2. (mathematics) Any real vector space on which a real-valued inner product (and, consequently, a metric) is defined.

Synonyms

• Cartesian space

Hypernyms

• Hilbert space
• inner product space
• real vector space

Translations

ordinary space

• Czech: euklidovský prostor m
• Danish: euklidisk rum n
• Finnish: euklidinen avaruus
• French: espace euclidien (fr) m
• Greek: Ευκλείδειος χώρος m (Efkleídeios chóros)
• Hungarian: euklideszi tér (hu)
• Japanese: ユークリッド空間 (ja) (Yūkuriddo kūkan)
• Korean: 유클리드 공간 (yukeullideu gonggan)
• (deprecated template usage) {{trans-mid}}
• Polish: przestrzeń euklidesowa f
• Portuguese: espaço euclidiano m
• Romanian: spațiu euclidian n
• Russian: евкли́дово простра́нство n (jevklídovo prostránstvo)
• Serbo-Croatian: euklidski prostor m
• Spanish: espacio euclídeo (es) m, espacio euclidiano m
• Swedish: euklidiskt rum n
• Thai: ปริภูมิแบบยุคลิด

type of vector space

• Korean: 유클리드 공간 (yukeullideu gonggan)
• (deprecated template usage) {{trans-mid}}