Projective View
In traditional geometry, affine geometry is considered to be a study between Euclidean geometry and projective geometry. On the one hand, affine geometry is Euclidean geometry with congruence left out; on the other hand, affine geometry may be obtained from projective geometry by the designation of a particular line or plane to represent the points at infinity. In affine geometry, there is no metric structure but the parallel postulate does hold. Affine geometry provides the basis for Euclidean structure when perpendicular lines are defined, or the basis for Minkowski geometry through the notion of hyperbolic orthogonality. In this viewpoint, an affine transformation geometry is a group of projective transformations that do not permute finite points with points at infinity.
Read more about this topic: Affine Geometry
Famous quotes containing the word view:
“Books of natural history aim commonly to be hasty schedules, or inventories of God’s property, by some clerk. They do not in the least teach the divine view of nature, but the popular view, or rather the popular method of studying nature, and make haste to conduct the persevering pupil only into that dilemma where the professors always dwell.”
—Henry David Thoreau (1817–1862)