affine geometry

In mathematics, affine geometry is the study of parallel lines.

Affine geometry can be developed on the basis of linear algebra.

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.

Several axiomatic approaches to affine geometry have been put forward:

In affine geometry, there is no metric structure but the parallel postulate does hold.

Ordered geometry is a common foundation of both absolute and affine geometry.

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.

These properties are studied by affine geometry, which is more general that Euclidean one, and can be generalized to higher dimensions.

Hence shape is an invariant of affine geometry.

The text is limited to affine geometry since projective geometry was put off to a second volume that did not appear.

The mathematical model of spacetime is an affine geometry equipped with a quadratic form that measures intervals between events.

Vector spaces stem from affine geometry, via the introduction of coordinates in the plane or three-dimensional space.

Affine geometry of curves - the study of curves in affine space.

In affine geometry, the relation of parallelism may be adapted so as to be an equivalence relation.

Projective geometry is less restrictive than either Euclidean geometry or affine geometry.

The simplest being projective, then the affine geometry which forms the intermediate layers and finally Euclidean geometry.

An 'affine hyperplane' is an affine space of codimension 1 in an affine geometry.

He uses affine geometry to introduce vector addition and subtraction at the earliest stages of his development of mathematical physics.

Projective geometry can be viewed as affine geometry with vanishing points (points at infinity) added.

In this context of affine geometry, in which angles are not differentiated, its definition admits only parallelograms and parallelepipeds.

At MathPath he has taught breakouts in Affine Geometry and Probability.

A concept of parallelism, which is preserved in affine geometry, is not meaningful in projective geometry.

In traditional geometry, affine geometry is considered to be a study between Euclidean geometry and projective geometry.