affine geometry
短语仿射几何
词形变化
释义与例句
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1.
The branch of geometry dealing with what can be deduced in Euclidean geometry when the notions of line length and angle size are ignored.
不可数 数学 可数As an alternative to the axiomatic approach, affine geometry can be studied via the properties of affine transformations, which do not, in general, preserve distances or angles, but do preserve alignment of points and parallelism of lines.
The notion of parallelism remains central to affine geometry, in which the parallel postulate is replaced by Playfair's axiom, a version of the postulate that relies on neither distance nor angle size.
1940 [McGraw-Hill], E. T. Bell, The Development of Mathematics, 2017 [1992], Dover, page 265, To include affine geometry, Menger (1935) imposed on lattices a reasonable axiom of parallelism.
1953 [Addison-Wesley], Dirk J. Struik, Lectures on Analytic and Projective Geometry, 2014, Dover, page 108, And affine geometry itself can be considered as the geometry of all projective transformations which leave a line invariant.
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2.
A geometry that is otherwise Euclidean but disregards lengths and angle sizes.
可数 不可数