Projective Geometry 18 Homology and Higher Dimensional Projective Space

In this video we step up one dimension, and consider projections of the plane to itself from a three dimensional perspective. There are connections with perspective drawing, the laws of projective space, and the introduction of the homology concept. Using homologies we can consider our transforms from a completely two dimensions perspective. Here we see an important implication of Desargues Theorem. It is also amusing to observe the beautiful patterns which can be created by repeatedly performing homologies to the plane. Such processes are analogous to the scenarios we considered earlier where repeated perspective mappings were used to transform lines.

Some figures used are from "Projective Geomety: Creative Polarities In Space And Time" By Olive Whicher.

[polgomezriquelme]

Thanks a lot for these amazing videos, Richard!