Projective geometry may be defined as the study of features which do not change under projective transformations. This is one good reason to study such transforms. We begin by looking at simple cases where a projective transformation maps a line to itself. We focus upon how the number of fixed points depends upon the relative positions of the primitives, and also have the novel idea of using a ghosted circle to illustrate the displacement between the image and the object at different points on the line.
Protective geometry is deeper and more fundamental than standard euclidean geometry, and has many applications in fundamental physics, biology and perspective drawing. We shall introduce it visually, without relying upon equations. The hope is make this beautiful subject accessible to anybody, without requiring prior knowledge of mathematics. At the same time, there are some very deep, rarely discussed ideas in this subject which could also benefit experts.