Euclidean Space
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This site looks at mathematics and how it can be computed.
Euclidean space. The hyper volume of the enclosed space is. A metric space that is linear. Solomentsev originator which appeared in encyclopedia of mathematics isbn 1402006098. Ordinary two or three dimensional space.
We now know through the theorms of kirt goedel that there is no definative way to clasifiy mathematics so the organisation here is abitary in some ways and reflects my own. The set of points in euclidean 4 space having the same distance r from a fixed point p 0 forms a hypersurface known as a 3 sphere. Euclidean space 3 this picture really is more than just schematic as the line is basically a 1 dimensional object even though it is located as a subset of n dimensional space. Since a vector space of dimension one is spanned by any nonzero vector a line is a set of the form where p and q are two distinct points.
Euclidean space is linear that is we can apply an algebraic structure called a vector space euclidean space is continuous differeniatable more about euclidean space on this page. The name of the site euclideanspace seems appropriate since euclid made one of the first attempts to document and classify the mathematics known at the time. Euclidean space synonyms euclidean space pronunciation euclidean space translation english dictionary definition of euclidean space. This article was adapted from an original article by ed.
Also a space in any finite number of dimensions in which points are designated by coordinates one for each dimension and the distance between two points is given by a distance formula. Euclidean space is flat that is euclids fifth postulate applies and right angled triangles obey pythagoras theorem. This segment is shown above in heavier ink. In addition the closed line segment with end points x and y consists of all points as above but with 0 t 1.
This is part of the friedmannlemaitrerobertsonwalker metric in general relativity where r is substituted by function rt with t meaning the cosmological age of the universe. Euclidean space euclidean space sometimes called cartesian space or simply space is the space of all n tuples of real numbers. Such tuples are sometimes called points although other nomenclature may be used see below. In a euclidean space a line is a euclidean subspace of dimension one.
