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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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Screenshot PDFs for my videos are available at the website wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.
My research papers can be found at my Research Gate page, at www.researchga...
My blog is at njwildberger.com/, where I will discuss lots of foundational issues, along with other things.
Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at www.openlearni... Please join us for an exciting new approach to one of mathematics' most important subjects!
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Here are the Insights into Mathematics Playlists:
• MathHistory: A course ...
• WildTrig: Intro to Rat...
• Math Foundations
• Wild Linear Algebra
• Famous Math Problems
• Box Arithmetic
• Elementary Mathematics...
• Year9Maths
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Here are the Wild Egg Maths Playlists (some available only to Members!)
• Algebraic Calculus One
• Classical to Quantum
• Algebraic Calculus Two
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• Playlist
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