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- Affine_geometry abstract "In mathematics, affine geometry is the study of parallel lines. Its use of Playfair's axiom is fundamental since comparative measures of angle size are foreign to affine geometry so that Euclid's parallel postulate is beyond the scope of pure affine geometry. In affine geometry, the relation of parallelism may be adapted so as to be an equivalence relation. Comparisons of figures in affine geometry are made with affinities, which are mappings comprising the affine group A. Since A lies between the Euclidean group E and the group of projectivities P, affine geometry is sometimes mentioned in connection with the Erlangen program, which is concerned with group inclusions such as E ⊂ A ⊂ P.Affine geometry can be developed on the basis of linear algebra. One can define an affine space as a set of points equipped with a set of transformations, the translations, which forms (the additive group of) a vector space (over a given field), and such that for any given ordered pair of points there is a unique translation sending the first point to the second. In more concrete terms, this amounts to having an operation that associates to any two points a vector and another operation that allows translation of a point by a vector to give another point; these operations are required to satisfy a number of axioms (notably that two successive translations have the effect of translation by the sum vector). By choosing any point as "origin", the points are in one-to-one correspondence with the vectors, but there is no preferred choice for the origin; thus this approach can be characterized as obtaining the affine space from its associated vector space by "forgetting" the origin (zero vector).".
- Affine_geometry thumbnail Translation_parallelogram.svg?width=300.
- Affine_geometry wikiPageExternalLink geombchap2.pdf.
- Affine_geometry wikiPageExternalLink pps2.pdf.
- Affine_geometry wikiPageID "243890".
- Affine_geometry wikiPageRevisionID "561118410".
- Affine_geometry hasPhotoCollection Affine_geometry.
- Affine_geometry subject Category:Affine_geometry.
- Affine_geometry comment "In mathematics, affine geometry is the study of parallel lines. Its use of Playfair's axiom is fundamental since comparative measures of angle size are foreign to affine geometry so that Euclid's parallel postulate is beyond the scope of pure affine geometry. In affine geometry, the relation of parallelism may be adapted so as to be an equivalence relation. Comparisons of figures in affine geometry are made with affinities, which are mappings comprising the affine group A.".
- Affine_geometry label "Affiene meetkunde".
- Affine_geometry label "Affine Geometrie".
- Affine_geometry label "Affine geometry".
- Affine_geometry label "Geometria affine".
- Affine_geometry label "Geometria afim".
- Affine_geometry label "Geometria afiniczna".
- Affine_geometry label "Geometría afín".
- Affine_geometry label "Géométrie affine".
- Affine_geometry label "Аффинная геометрия".
- Affine_geometry label "هندسة تآلفية".
- Affine_geometry label "仿射几何学".
- Affine_geometry sameAs Afinní_geometrie.
- Affine_geometry sameAs Affine_Geometrie.
- Affine_geometry sameAs Geometría_afín.
- Affine_geometry sameAs Géométrie_affine.
- Affine_geometry sameAs Geometria_affine.
- Affine_geometry sameAs Affiene_meetkunde.
- Affine_geometry sameAs Geometria_afiniczna.
- Affine_geometry sameAs Geometria_afim.
- Affine_geometry sameAs m.01kbvv.
- Affine_geometry sameAs Q382520.
- Affine_geometry sameAs Q382520.
- Affine_geometry wasDerivedFrom Affine_geometry?oldid=561118410.
- Affine_geometry depiction Translation_parallelogram.svg.
- Affine_geometry isPrimaryTopicOf Affine_geometry.
