The Arc Length Parameterization

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  • Опубліковано 23 гру 2024

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  • @Essentialsend
    @Essentialsend 6 місяців тому +5

    I am myself a Maths teacher. And there are very few teachers out there , I really like to listen to. You are one of them. Your way of presenting things is just perfect

  • @goobersteinmcfancyful
    @goobersteinmcfancyful 6 місяців тому +5

    I am desperately waiting for you to put together a full course on Differential Geometry of Curves and Surfaces and Beyond

    • @MathTheBeautiful
      @MathTheBeautiful  6 місяців тому +3

      ua-cam.com/play/PLlXfTHzgMRUKG7lkye7DQAmNB0cfWNgWG.html

  • @DivineScaleOfGod
    @DivineScaleOfGod 5 місяців тому

    I have two questions about surfaces. Is there a way to find the inverse of a surface? The other question is we have parametrization by arc lengh, but is there a way to define a parametrization by surface area?

  • @theoremus
    @theoremus 6 місяців тому

    The radian is related to arclength of the circle. Hence, to do angle measurement in radians, one needs differential geometry.

  • @pontifexmaximus_e
    @pontifexmaximus_e 6 місяців тому

    What textbook do you use please?

    • @MathTheBeautiful
      @MathTheBeautiful  6 місяців тому +1

      Writing one. It will soon be on grinfeld.org

  • @KaiseruSoze
    @KaiseruSoze 6 місяців тому

    Excellent as usual.
    How long is a line? Twice as long as a half of a line. Which one you choose as a reference length is arbitrary.

  • @alegian7934
    @alegian7934 6 місяців тому

    if we allow ourselves to think with an extra dimension, is there some "arc length parametrization" for 3d surfaces? like a square grid of unit length? then the second degree of freedom (orientation) actually becomes continuous aswell (any angle of rotation). idk, just a thought
    EDIT: now that I think about it, adding an extra dimension might break other things... what even is R(s+h)? h would have to have orientation.. I dont want to think about this anymore :)

    • @MathTheBeautiful
      @MathTheBeautiful  6 місяців тому +2

      This is actually a classical question that leads to the Riemann-Christoffel tensor

  • @punditgi
    @punditgi 6 місяців тому +1

    I love these videos! 😊

  • @godfreypigott
    @godfreypigott 6 місяців тому +2

    You might want to correct the spelling in your title.

  • @Pluralist
    @Pluralist 6 місяців тому

  • @cescllopis
    @cescllopis 6 місяців тому

    ME,I THINK IT SHOULD READ .Cf. e.g. . ROLF NEVANLINNA HAS WRITEN A BOOK WITH THE TITLE [GERMAN] SPRINGER -VERLAG ,1967 2.EDITION.