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Video shows what Euclidean space means. Ordinary two- or three-dimensional space, characterised by an infinite extent along each dimension and a constant distance between any pair of parallel lines.. Any real vector space on which a real-valued inner product (and, consequently, a metric) is defined.. Euclidean space synonyms: Cartesian space. Euclidean space Meaning. How to pronounce, definition audio dictionary. How to say Euclidean space. Powered by MaryTTS, Wiktionary