# Euclidean space

NOUN
1. a space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional
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## How To Use Euclidean space In A Sentence

• He worked on conjugate functions in multidimensional euclidean space and the theory of functions of a complex variable.
• However he continued to work on topological ideas, in particular embedding complexes in Euclidean space.
• He worked on conjugate functions in multidimensional euclidean space and the theory of functions of a complex variable.
• The essential property and developmental course of Euclidean space, symplectic space and bogus space are studied.
• In the classical differential geometry which deals with the theory of curves and surfaces of three dimensional Euclidean space, the most distinctive study is the Weingarten surface.
• On the foundation of the conception of orthonormal basis in finite dimensional Euclidean space, this paper provides the theory of completely orthonormal system in infinite dimensional Euclidean space.
• Up to this stage quantum theory was set up in Euclidean space and used Cartesian tensors of linear and angular momentum.
• A few good necessary and sufficient conditions are given by using length relation for symmetrical transformation on Euclidean space.
• A familiar Riemannian manifold is a Euclidean manifold (where one has to add a smoothly varying inner product on the tangent space of the standard Euclidean space), with the familiar Euclidean (distance) metric (our 3-space, for example). Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element
• Also, the precise mathematical form Poincaré chose had to make the Poincaré-line that joins any two points the shortest path between them called a geodesic, just as the usual line is the shortest path between points in Euclidean space. Euclid’s Window
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