We continue our study of projective transformations of the line, and study what configurations cause involutions. An involution is a transformation which leaves positions unaltered, when applied twice. Interestingly, our questions about involutions quickly return us to the consideration of harmonic quadrilaterals.
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.