Theory of numbers: Euclid's algorithm

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  • Опубліковано 29 гру 2024

КОМЕНТАРІ • 16

  • @anthonymurphy5689
    @anthonymurphy5689 3 роки тому +16

    Richard always brings an interesting perspective to even the most well-trodden subject.

    • @john-r-edge
      @john-r-edge 3 роки тому

      His explanation of why "1" is not a prime was excellent.

  • @kichelmoon6365
    @kichelmoon6365 Місяць тому

    Thank you so much for your content, you have an incredibily captivating way of presenting things

  • @peterboneg
    @peterboneg 3 роки тому +5

    Well explained. It's also nice to see how Euclid did it. Just a note that I think you may have got a and b reversed at 9:00.

  • @robharwood3538
    @robharwood3538 3 роки тому +4

    I suppose the remaining videos in the playlist are marked private because they will be made public at a later time (like a release schedule)? Just letting you know that the playlist does show them, but they are marked as private and no details about them are visible (just their presence in the list). Cheers! Thanks for the lecture. I learned method 4 from it, which I had not heard of before!

  • @ans1975
    @ans1975 3 роки тому +1

    The beatifully sober video style is ideal
    from a cognitive point of view: as an effect
    it is very easy to follow and concentrate on the (amazing) content...

  • @philkaw
    @philkaw 3 роки тому

    5:32
    Wouldn't it be linear instead since #digits of a is roughly log(a), so k^log(a) would be proportional to the input a?

    • @martinepstein9826
      @martinepstein9826 3 роки тому +2

      The size of the input is proportional to # digits of a, not a. It's defined as the number of bits when you write a in binary.

    • @hywelgriffiths5747
      @hywelgriffiths5747 3 місяці тому

      The question is right: the time taken is linear in a since as you can see it written there, time is ~ a steps, but because computational time is usually given as a function of # digits (which is indeed of order log(a)), it's an exponential function

  • @isaacchen9408
    @isaacchen9408 3 роки тому +1

    Method 4 is really neat! Any source who used it first? Thank you professor Borcherds!

    • @isaacchen9408
      @isaacchen9408 3 роки тому

      "Computational problems associated with Racah algebra" by J. Stein
      Vol 1, Issue 3, Feb 1967, pp 397-405, Journal of Computational Physics
      Should have done my homework before asking! 🙂

  • @mikegallegos7
    @mikegallegos7 3 роки тому

    That was very cool.
    Thank you.

  • @john-r-edge
    @john-r-edge 3 роки тому

    Those of us from the UK with sufficient chronological endurance were taught long division of pounds, shillings and pence. And that was really hard.

  • @mahmudulhasan.turjoy
    @mahmudulhasan.turjoy 3 роки тому

    nice lecture.

  • @Mathin3D
    @Mathin3D 3 роки тому +1

    Method 4 begs for some properties of the gcd to precede this lesson.

  • @migarsormrapophis2755
    @migarsormrapophis2755 3 роки тому +2

    yeee
    ye