affine geometry การใช้

• Affine geometry can also be developed on the basis of linear algebra.
• When parallel lines are taken as primary, synthesis produces affine geometry.
• Ordered geometry is a common foundation of both absolute and affine geometry.
• The concept of a polytope belongs to affine geometry, which is more general than Euclidean.
• After Felix Klein's Erlangen program, affine geometry was recognized as a generalization of Euclidean geometry.
• The various types of affine geometry correspond to what interpretation is taken for " rotation ".
• Affine geometry is one of the two main branches of classical algebraic geometry, the other being projective geometry.
• Parallelism is primarily a property of affine geometries and Euclidean space is a special instance of this type of geometry.
• In particular, Euclidean geometry was more restrictive than affine geometry, which in turn is more restrictive than projective geometry.
• More general affine manifolds or affine geometries are obtained easily by dropping the flatness condition expressed by the Maurer-Cartan equations.
• In 1912, Edwin B . Wilson and Gilbert N . Lewis developed an affine geometry to express the special theory of relativity.
• The extra flexibility thus afforded makes affine geometry appropriate for the study of spacetime, as discussed in the history of affine geometry.
• The extra flexibility thus afforded makes affine geometry appropriate for the study of spacetime, as discussed in the history of affine geometry.
• Comparisons of figures in affine geometry are made with affine transformations, which are mappings that preserve alignment of points and parallelism of lines.
• It follows that rays exist only for geometries for which this notion exists, typically Euclidean geometry or affine geometry over an ordered field.
• This axiom is used not only in Euclidean geometry but also in the broader study of affine geometry where the concept of parallelism is central.
• Some examples of axiomatized systems of geometry include ordered geometry, absolute geometry, affine geometry, Euclidean geometry, projective geometry, and hyperbolic geometry.
• Affine geometry can be viewed as the geometry of an affine space of a given dimension " n ", coordinatized over a synthetic finite geometry.
• At Wesleyan University he led a group that developed a course of geometry for high school students that treated Euclidean geometry as a special case of affine geometry.
• More generally, the properties of flats and their incidence of Euclidean space are shared with affine geometry, whereas the affine geometry is devoid of distances and angles.