affine geometry in a sentence
1) In mathematics, affine geometry is the study of parallel lines.
affine collocations
2) Projective geometry is less restrictive than either Euclidean geometry or affine geometry .
3) Affine geometry and projective geometry have not a distinct notion of rotation.
affine geometry example sentences
4) In affine geometry , there is no metric structure but the parallel postulate does hold.5) The various types of affine geometry correspond to what interpretation is taken for "rotation".
6) The concept of a polytope belongs to affine geometry , which is more general than Euclidean.
7) Vector spaces stem from affine geometry via the introduction of coordinates in the plane or three-dimensional space.
8) In traditional geometry, affine geometry is considered to be a study between Euclidean geometry and projective geometry.
9) The mathematical model of spacetime is an affine geometry equipped with a quadratic form that measures intervals between events.
10) After Felix Klein's Erlangen program, affine geometry was recognized as a generalization of Euclidean geometry.
11) In affine geometry , the relation of parallelism may be adapted so as to be an equivalence relation.
12) He uses affine geometry to introduce vector addition and subtraction at the earliest stages of his development of mathematical physics.
13) In 1918, Hermann Weyl referred to affine geometry for his text "Space, Time, Matter".
14) More general affine manifolds or affine geometries are obtained easily by dropping the flatness condition expressed by the Maurer-Cartan equations.
15) In 1827, August Möbius wrote on affine geometry in his "Der barycentrische Calcul" (chapter 3).
example sentences with affine geometry
16) Comparisons of figures in affine geometry are made with affinities, which are mappings comprising the affine group "A".17) It follows that rays exist only for geometries for which this notion exists, typically Euclidean geometry or affine geometry over an ordered field.
18) The pair ("P",η) defines the structure of an affine geometry on "M", making it into an affine manifold.
19) In this viewpoint, an affine transformation geometry is a group of projective transformations that do not permute finite points with points at infinity.
20) Affine geometry can be viewed as the geometry of an affine space of a given dimension "n", coordinatized over a field "K".
21) Several axiomatic approaches to affine geometry have been put forward:
22) General affine geometries : formal definitions
23) An axiomatic treatment of plane affine geometry can be built from the axioms of ordered geometry by the addition of two additional axioms:
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