In this video we extend the discussion of curvature from parabolas to more general conics, and hence to more general algebraic curves. The advantage of basing things on the parabola is that we get nice connections between curvature and the foci, and that once we move to studying surfaces in three dimensional space, the normal paraboloids will play an exactly analogous role as do the normal parabolas here.

This lecture does have quite a lot of formulas in it, because we are interested in laying out technology that will easily allow us to move from one view to another. At some point, we begin to appreciate the power of formulas in pinning down this subject, but it does help to develop some sympathy with algebraic relations!

A point of divergence from the usual formulation: we emphasize the usefulness in thinking about the square of the usual curvature. This quadratic curvature can be formulated without any appeal to square roots.

Correction: That equation at 18:58 should have the factor (mx-ly)^2, not (lx-my)^2 (it can be properly remembered by being a cross product term). Following on, the next equation should also have the same correction. Thanks Thomas Fuhrmann!

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Screenshot PDFs for my videos are available at the website [ Ссылка ]. 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 [ Ссылка ]

My blog is at [ Ссылка ], 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 [ Ссылка ] 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:

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Here are the Wild Egg Maths Playlists (some available only to Members!)

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