Mathematical space and a basic duality in geometry | Rational Geometry Math Foundations 122

In this video we introduce some basic orientation to the problem of how we represent, and think about, space in mathematics. One key idea is the fundamental duality between the affine and projective views: two sides of the same coin.

We explain how the Cartesian revolution of the 17th century built geometry from a prior theory of arithmetic: for us that of the rational numbers- of course!

And we introduce some useful notations for points and proportions, and give a geometrical view of the relation between the affine line and the projective line.

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Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.

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My blog is at http://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 https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects!

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