Euclidean
[yoo-klid-ee-uh n] /yuˈklɪd i ən/
adjective
1.
of or relating to Euclid, or adopting his postulates.
adj.
1650s, “of or pertaining to Euclid,” from Greek Eukleides, c.300 B.C.E. geometer of Alexandria. Now often used in contrast to alternative models based on rejection of some of his axioms. His name in Greek means “renowned,” from eu “well” (see eu-) + kleos “fame” (see Clio).
Euclidean
(y-klĭd’ē-ən)
Relating to geometry of plane figures based on the five postulates (axioms) of Euclid, involving the derivation of theorems from those postulates. The five postulates are: 1. Any two points can be joined by a straight line. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line segment, a circle can be drawn having the line segment as radius and an endpoint as center. 4. All right angles are congruent. 5. (Also called the parallel postulate.) If two lines are drawn that intersect a third in such a way that the sum of inner angles on one side is less than the sum of two right triangles, then the two lines will intersect each other on that side if the lines are extended far enough. Compare non-Euclidean.
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- Euclidean-geometry
noun 1. geometry based upon the postulates of Euclid, especially the postulate that only one line may be drawn through a given point parallel to a given line.
- Euclidean-group
noun, Mathematics. 1. the set of rigid motions that are also affine transformations.
- Euclidean norm
mathematics The most common norm, calculated by summing the squares of all coordinates and taking the square root. This is the essence of Pythagoras’s theorem. In the infinite-dimensional case, the sum is infinite or is replaced with an integral when the number of dimensions is uncountable. (2004-02-15)
- Euclidean-space
noun, Mathematics. 1. ordinary two- or three-dimensional space. 2. any vector space on which a real-valued inner product is defined.