The perspective image of a square I | Famous Math Problems 18a) | N J Wildberger

Описание: In this episode of Famous Math Problems, we look at the lovely solved problem: how to show that any quadrilateral is the perspective image of a square. This is a question of 3 dimensional projective geometry, but it has a Euclidean aspect because the idea of a square is crucial. In this video we lay some of the groundwork, reviewing basic facts of projective geometry, including the relationships between quadrilaterals (4 planar points) and quadrangles (4 planar lines), more generally the idea of duality between points and lines, and the cross ratio.

This last concept we will introduce in a somewhat novel way, following the approach outlined in the Algebraic Calculus One course, where the cross product of planar vectors plays a key role.

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