Explore advanced concepts in Projective Geometry through this in-depth video lecture. Investigate the problem of showing how a general quadrilateral can be the perspective image of a square. Examine the role of vanishing points and lines at infinity in both two-dimensional and three-dimensional projections. Learn about parallel projections and their relationship to perspectivity, and discover how to accurately represent perspective images. Delve into Desargues' famous theorem in its three-dimensional form. Cover topics including planar perspectivity, flexible positioning in projections, 3D coordinate systems, and Desargues' configuration in space and the plane.
Perspective Image of a Square - More Projective Geometry - Lecture 18b
Insights into Mathematics via YouTube
Overview
Syllabus
The perspective image of a square
Planar perspectivity
The relative positions of P,__ are flexible
Mathematical diagrams with 3D co-ordinate systems and parallel projections
Three dimensional perspectivity
Desargues' configuration in space
Desargues' theorem in the plane
Taught by
Insights into Mathematics
