Projective geometry

A branch of pure mathematics that is concerned with the geometrical properties (distinguished by a peculiar interrelatedness and stability) that are preserved under arbitrary projective transformations of the plane (or of space). As a non-metrical geometry (not restricted to the Euclidean geometrical concepts of length, angles, area and volume), it is primarily concerned with the concepts of point, line and plane, and their interrelationships, without the need for measure. As such, it is not merely a geometry of created forms, but the geometry of form-creating entities. It enters the domain of movement and metamorphosis, where rigid measure is no longer the dominating factor, and one form can change into another without losing its identity. It requires a qualitative grasp of mathematical form before it takes on a fixed shape in the quantitative field of measure. It has a unifying effect on the whole field of geometry in that it is concerned with the whole, whereas the metrical geometries deal only with the part.