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!)

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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.

    My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger

    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/algebraic-calculus-one/ 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 https://www.patreon.com/njwildberger Your support would be much appreciated.

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    Here are all the Insights into Mathematics Playlists:

    Elementary Mathematics (K-6) Explained: https://www.youtube.com/playlist?
    list=PL8403C2F0C89B1333
    Year 9 Maths: https://www.clipvl.net/p/PLIljB45xT85CcGpZpO542YLPeDIf1jqXK
    Ancient Mathematics: https://www.clipvl.net/p/PLIljB45xT85Aqe2b4FBWUGJdYROT6-o4e
    Wild West Banking: https://www.clipvl.net/p/PLIljB45xT85DB7CzoFWvA920NES3g8tJH
    Sociology and Pure Mathematics: https://www.clipvl.net/p/PLIljB45xT85A-qCypcmZqRvaS1pGXpTua
    Old Babylonian Mathematics (with Daniel Mansfield): https://www.youtube.com/playlist?
    list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
    Math History: https://www.clipvl.net/p/PL55C7C83781CF4316
    Wild Trig: Intro to Rational Trigonometry: https://www.clipvl.net/p/PL3C58498718451C47
    MathFoundations: https://www.clipvl.net/p/PL5A714C94D40392AB
    Wild Linear Algebra: https://www.clipvl.net/p/PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp
    Famous Math Problems: https://www.clipvl.net/p/PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf
    Probability and Statistics: An Introduction: https://www.clipvl.net/p/PLIljB45xT85AMigTyprOuf__daeklnLse
    Boole's Logic and Circuit Analysis: https://www.clipvl.net/p/PLIljB45xT85CnIGIWb7tH1F_S2PyOC8rb
    Universal Hyperbolic Geometry: https://www.clipvl.net/p/PLIljB45xT85CN9oJ4gYkuSQQhAtpIucuI
    Differential Geometry: https://www.clipvl.net/p/PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP
    Algebraic Topology: https://www.clipvl.net/p/PL6763F57A61FE6FE8
    Math Seminars: https://www.clipvl.net/p/PLBF39AFBBC3FB30AF
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    And here are the Wild Egg Maths Playlists:

    Triangle Centres: https://www.clipvl.net/video/iLBGXDSUohM/video.html
    Six: An elementary course in pure mathematics: https://www.clipvl.net/p/PLzdiPTrEWyz4KD007Ge10dfrDVc4YwlYS
    Algebraic Calculus One: https://www.clipvl.net/p/PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB
    Algebraic Calculus Two: https://www.clipvl.net/p/PLzdiPTrEWyz5VLVr-0LPPgm4T1mtU_DG-
    м
  • Source: https://youtu.be/_mvjOoTieTk
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