## affine geometry

57 examples (0.02 sec)
• The text is limited to affine geometry since projective geometry was put off to a second volume that did not appear.
• Ordered geometry is a common foundation of both absolute and affine geometry.
• When parallel lines are taken as primary, synthesis produces affine geometry.
• The various types of affine geometry correspond to what interpretation is taken for rotation.
• In affine geometry, there is no metric structure but the parallel postulate does hold.
• In mathematics, affine geometry is the study of parallel lines.
• Affine geometry can be developed on the basis of linear algebra.
• He uses affine geometry to introduce vector addition and subtraction at the earliest stages of his development of mathematical physics.
• The following proof uses only notions of affine geometry, notably homothecies.
• The concept of a polytope belongs to affine geometry, which is more general than Euclidean.
• Vector spaces stem from affine geometry via the introduction of coordinates in the plane or three-dimensional space.
• In affine geometry, the relation of parallelism may be adapted so as to be an equivalence relation.
• Projective geometry can be viewed as affine geometry with vanishing points (points at infinity) added.
• Experimental designs were also studied with affine geometry over finite fields and then with the introduction of association schemes by R. C. Bose.
• 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.
• It follows that rays exist only for geometries for which this notion exists, typically Euclidean geometry or affine geometry over an ordered field.
• In traditional geometry, affine geometry is considered to be a study between Euclidean geometry and projective geometry.
• The simplest being projective, then the affine geometry which forms the intermediate layers and finally Euclidean geometry.
• For example, affine geometry does not see the difference between an equilateral triangle and a right triangle, but in Euclidean space the former is regular and the latter is not.
• Since the axioms of ordered geometry as presented here include properties that imply the structure of the real numbers, those properties carry over here so that this is an axiomatization of affine geometry over the field of real numbers.