4.6 Dynamic Illustrations for Perspectivity
The only way to learn mathematics is to do mathematics.
—Paul Halmos (1916–2006)

A one-to-one mapping between a pencil of points and a pencil of lines is called an elementary correspondence if each point of the pencil of points is incident with the corresponding line of the pencil of lines.

A one-to-one mapping between two pencils of points is called a perspectivity if the lines incident with the corresponding points of the two pencils are concurrent. The point where the lines intersect is called the center of the perspectivity.

A one-to-one mapping between two pencils of lines is called a perspectivity if the points of intersection of the corresponding lines of the two pencils are collinear. The line containing the points of intersection is called the axis of the perspectivity.

Note that a perspectivity is a composition of two elementary correspondences between either two pencils of points or two pencils of lines.

4.6 Definitions
 
     
© Copyright 2013 - Timothy Peil