Projectivisuus

Projectivisuus is a term used in mathematics, particularly in projective geometry, to describe a property related to how geometric objects are mapped or projected. It essentially refers to the concept of projection itself and the preservation of certain relationships under such projections. In a projective space, lines remain lines, and the collinearity of points is preserved. This means that if several points lie on the same line in one plane, their projections onto another plane will also lie on a single line.

The fundamental idea behind projectivisuus is the existence of a mapping, a projection, from one geometric space to another. This mapping typically involves a center of projection and a projection plane. Points on a line passing through the center of projection are mapped to a single point on the projection plane. The study of projectivisuus aims to understand the invariants and transformations that occur under these projective mappings.

This concept is crucial for understanding concepts like perspective drawing, where a three-dimensional scene is projected onto a two-dimensional canvas, or in understanding the relationships between different geometric figures in projective geometry. It allows for the study of geometric properties that are invariant under projection, regardless of the specific position or orientation of the projected objects. The underlying principle is the way objects are "seen" or "cast" from one space to another.