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In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance...

parallel line segments. Affine space is the setting for affine geometry. As in Euclidean space, the fundamental objects in an affine space are called points...

In Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines...

in the set. Projective geometry can be viewed as affine geometry with vanishing points (points at infinity) added. An affine hyperplane together with...

Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate...

Kaluza's five-dimensional theory, and Eddington's development of affine geometry. Einstein corresponded with these researchers, and collaborated with...

elliptic, spherical or affine geometry. Axioms of continuity and "betweenness" are also optional, for example, discrete geometries may be created by discarding...

19th century, such as non-Euclidean, projective, and affine geometry. In the Greek deductive geometry of Euclid's Elements, a general line (now called a...

obtained by extending the notion of point: In classical algebraic geometry, a point of an affine variety may be identified, through Hilbert's Nullstellensatz...

Affine differential geometry is a type of differential geometry which studies invariants of volume-preserving affine transformations. The name affine...

of affine geometries and Euclidean geometry is a special instance of this type of geometry. In some other geometries, such as hyperbolic geometry, lines...

bioinformatics Affine geometry, a geometry characterized by parallel lines Affine group, the group of all invertible affine transformations from any affine space...

inversive geometries. Finite geometries may be constructed via linear algebra, starting from vector spaces over a finite field; the affine and projective...

In geometry, Brianchon's theorem is a theorem stating that when a hexagon is circumscribed around a conic section, its principal diagonals (those connecting...

Absolute geometry Affine geometry Algebraic geometry Analytic geometry Birational geometry Complex geometry Computational geometry Conformal geometry Constructive...

Agustí. "Affine Maps, Euclidean Motions and Quadrics". Springer, 2011, ISBN 978-0-85729-709-9, page 11 Deaux, Roland. "Introduction to The Geometry of Complex...

two-dimensional half-space. A half-plane can be split in two quadrants. The affine transformations of the upper half-plane include shifts ( x , y ) ↦ ( x +...