Duality, Projective Geometry And Circle Inversion

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  • เผยแพร่เมื่อ 30 ก.ย. 2024
  • In this video I introduce projective geometry by discussing points at infinity, point-line duality, polarities and circle inversion.

ความคิดเห็น • 16

  • @alan2here
    @alan2here 3 ปีที่แล้ว +8

    Thanks for using the animations, it makes it nice and clear.

  • @thomasolson7447
    @thomasolson7447 3 ปีที่แล้ว +1

    Judging by your play list I think you might like my avatar and banner. The spectrum is fun and all but I think the RGB spectrum (unsure what to call it) is just as interesting. My video "Mandelbrot Tutorial with Javascript and Maple" kind of address it.

  • @xandermoyle
    @xandermoyle 10 หลายเดือนก่อน

    Perhaps if you view a line on either end at an infinite distance it will appear as a point.

  • @brendanmccann5695
    @brendanmccann5695 3 ปีที่แล้ว +1

    What a fantastic video! Great, great, great! Thank you.

  • @avi3681
    @avi3681 3 ปีที่แล้ว +1

    Very beautiful and clearly explained. I love the animations and the math. What software are you using?

    • @RichardSouthwell
      @RichardSouthwell  3 ปีที่แล้ว +1

      Kind of you to say. Circle inversion is really interesting. There is an excellent numberphile video about it (epic circles). I used geogebra.

    • @avi3681
      @avi3681 3 ปีที่แล้ว

      @@RichardSouthwell Have you seen this video about Coxeter and M.C. Escher
      th-cam.com/video/JkhuMvFQWz4/w-d-xo.html

    • @RichardSouthwell
      @RichardSouthwell  3 ปีที่แล้ว +1

      @@avi3681 That was good. I did not know that about circle inversion of an equiangular spiral. Wildberger's video on Ford circles is another interesting one somewhat related to circle inversion.

    • @phiarchitect
      @phiarchitect 3 ปีที่แล้ว +1

      @@avi3681 The Coxeter Escher video is terrific! Thanks for pointing it out.

  • @astroceleste292
    @astroceleste292 2 ปีที่แล้ว

    can you put subtitles? the automatic captions are crap for mathematical terms.

  • @chandankar5032
    @chandankar5032 3 ปีที่แล้ว

    Sir i am a undergrad ,and i want to do a small project on projective geometry ,emphacising the role of linear algebra ,i took a look at the book ,"Linear Algebra and Projective geometry by Reinhold Baer" ,but found it preety extensive,full of techniaclities and way much comphresive for a single project. Can you suggest something more simpler highlighting the use of linear algebra ?

    • @RichardSouthwell
      @RichardSouthwell  3 ปีที่แล้ว

      www.amazon.co.uk/Introduction-Projective-Geometry-Dover-Mathematics/dp/048646895X

    • @RichardSouthwell
      @RichardSouthwell  3 ปีที่แล้ว

      you can go straight to the chapter using homogeneous coordinates

  • @leofun01
    @leofun01 ปีที่แล้ว

    Turn the volume up