Classical curves | Differential Geometry 1 | NJ Wildberger

Classical curves | Differential Geometry 1 | NJ Wildberger

The first lecture of a beginner’s course on Differential Geometry! Given by Assoc Prof N J Wildberger of the School of Mathematics and Statistics at UNSW. Differential geometry is the application of calculus and analytic geometry to the study of curves and surfaces, and has numerous applications to manufacturing, video game design, robotics, physics, mechanics and close connections with classical geometry, algebraic topology, the calculus of several variables and mostly notably Einstein’s General Theory of Relativity.

This lecture summarizes the basic topics of the course, the unique point of view of the lecturer, and then heads straight into a survey of classical curves, starting with the line, then the conic sections (ellipse, parabola, hyperbola), then moving to classical ways of generating new curves from old ones. These techniques include the Conchoid construction of Nicomedes, the Cissoid construction of Diocles, the Pedal curve construction and the evolute and involute introduced by Huygens. This lecture should be viewed in conjunction with MathHistory16: Differential Geometry.

If your level of mathematics is roughly that of an advanced undergraduate, then please come join us; we are going to look at lots of interesting classical topics, but with a modern, lively new point of view. There will be opportunities for you to contribute to new directions. Prepare to be surprised, for our approach follows that famous Zen saying:

“In the beginner’s mind there are many possibilities; in the expert’s mind there are few.”

The music is by Exchange: a track called Take Me Higher (thanks Steve Sexton!)

My research papers can be found at my Research Gate page, at I also have a blog at where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at Of course if you want to support all these bold initiatives, become a Patron of this Channel at .

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  1. This is an excellent presentation and reminds me a lot of the course I took on differential geometry at UW-Milwaukee some years ago. Im going over the material again to refresh and your videos are very helpful.

    I should also mention that I've bern working on something that i call a "dualistic topology", which can be explained in just one sentence. We make a new kind of Fuzzy Logic on the assumption that the discrete set {0,1} and the open interval (0,1) are Equivalent . ..in the sense of Relativity.

    This, I know, is extremely unorthodox and controversial. But the consequences are pretty amazing and it seems to ecplain a lot of QM.

    Anyway, thanks for your great videos and keep up the good work.

  2. Profossor, are your lectures 'WildTrig' and 'UHG' needed for this lectures?
    I'm actually learning Special relativity and General relativity courses at my university. But I have no backgrounds of geometrical methods for the Relativity course. So I was going to study DE by yours…

  3. The example shown for a pedal curve of a parabola is not shown correctly. If the parabola opens downward, you get a Cissoid of Diocles. For the parabola shown, the cissoid would appear below the parabola. Bob

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