Classical curves | Differential Geometry 1 | NJ Wildberger

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  • Published on:  Thursday, August 1, 2013
  • The first lecture of a beginner's course on Differential Geometry! Given by 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!)

    Screenshot PDFs for my videos are available at the website 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

    My blog is at, where I will discuss lots of foundational issues, along with other things.

    Online courses will be developed at The first one, already underway is Algebraic Calculus One at Please join us for an exciting new approach to one of mathematics' most important subjects!

    If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at Your support would be much appreciated.

    Here are all the Insights into Mathematics Playlists:

    Elementary Mathematics (K-6) Explained:
    Year 9 Maths:
    Ancient Mathematics:
    Wild West Banking:
    Sociology and Pure Mathematics:
    Old Babylonian Mathematics (with Daniel Mansfield):
    Math History:
    Wild Trig: Intro to Rational Trigonometry:
    Wild Linear Algebra:
    Famous Math Problems:
    Probability and Statistics: An Introduction:
    Boole's Logic and Circuit Analysis:
    Universal Hyperbolic Geometry:
    Differential Geometry:
    Algebraic Topology:
    Math Seminars:

    And here are the Wild Egg Maths Playlists:

    Triangle Centres:
    Six: An elementary course in pure mathematics:
    Algebraic Calculus One:
    Algebraic Calculus Two:
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