The Perspective Image of a Square - Famous Math Problems 18a

Explore the fascinating problem of proving that any quadrilateral is the perspective image of a square in this lecture on 3D projective geometry. Delve into the foundational concepts of projective geometry, including the relationships between quadrilaterals and quadrangles, the principle of duality between points and lines, and the cross ratio. Learn about a novel approach to introducing the cross ratio using the cross product of planar vectors, as outlined in the Algebraic Calculus One course. Gain insights into this solved mathematical problem that combines elements of projective geometry with Euclidean concepts, setting the groundwork for further exploration of this intriguing topic.