Comments by "Lawrence D’Oliveiro" (@lawrencedoliveiro9104) on "Mathologer" channel.

  1. I tried doing the same. Not long after that I discovered computer programming. And I figured out how to do a first-order binary search between two points on the curve, one with positive Y and the other with negative Y, looking for the zero point. And I also figured out that the solutions for the (n+1)-degree polynomial, if they existed, lay between those for the n-degree polynomial which was its derivative. All this was before I actually got my hands on a computer for the first time.
    46
  2. A joke for linguists: Carissimus Dei.
    33
  3. 16:14 One thing that makes this sort of thing easier nowadays is the existence of interactive languages like Python that have built-in infinite-precision integer arithmetic. No rounding errors if you avoid fractions!
    10
  4. I should add, mathematicians can use both notations: I believe it’s superscripts for column vectors, and subscripts for row vectors.
    6
  5. 31:30 You haven’t explained how these equilateral triangles arise. They come about from dividing the angle by 3: you can add or subtract any number of complete circles (2π radians) to/from the original angle and it is still the same, but when those complete circles are divided by 3, they offset the resulting angle by ±2π/3 or ±120°, giving you the 3 vertices of the equilateral triangle.
    3
  6. 5:17 One of the luminaries from the Islamic Golden Age, back when Europe was still in the Dark Ages.
    3
  7. /me pulls string on Talking Barbie Doll “Math is hard!” Moral: don’t get life lessons from a Talking Barbie Doll.
    3
  8. Newton’s BDSM law: to every whip action, there is a chain reaction.
    2
  9.  @hachikiina  Not lost https://www.aljazeera.com/programmes/science-in-a-golden-age/
    2
  10.  @rucker69  My 1970s-vintage TI-58C could show 12 digits, and actually calculated internally to a bit more than that.
    2
  11.  @rucker69  My 1970s-vintage TI-58C could show 12 digits, and actually calculated internally to a bit more than that.
    2
  12. It seems pretty clear (to me at least) that Newton and Leibnitz came up with it independently, because they invented completely different notations for it. And Leibnitz’ notation is actually superior.
    2
  13. Cool. I think I actually understood that. ;)
    1
  14. 9:45 Spot the fine-structure constant!
    1
  15. 15:07 the CDC 6000 series were designed by computer hardware genius Seymour Cray. The company was set up to sell conventional business machines, and really had no idea what to do with the fastest computers in the world that he had created for them. Competitor IBM also hated them and tried to kill the company. Today, it appears there is just one 6000-series machine still operating in the whole world: https://www.youtube.com/watch?v=4Zt03YsMyW4 Cray later left CDC to form his own company to concentrate on making supercomputers. You may have heard of it ... what was it called again ...
    1
  16. 18:51 He meant “chaotic”.
    1
  17. 1:47 As the point on the handle gets closer to the middle screw, the ellipse gets more and more eccentric, until at the screw, it becomes a line (horizontal in the video). Further along towards the other screw, its eccentricity is reduced until it reaches zero at the midpoint (perfect circle), then increases again, this time the ellipses are squashed the other way, until at the end screw, the shape traced becomes a line that is vertical in the video. Beyond that the eccentricity reduces again, but it won’t reach zero until you get to an infinite distance.
    1
  18. 3:17 At this point, I’d guess that you can have any integer number of slider axes ≥ 2, and furthermore they don’t even have to be distributed at uniform angles (subject only to the mechanical limitations of actually building a physically possible shape). As the centre point between the pivots always lies on a 4D* linear spiral, a projection of that world line along any axis will produce a sine wave. Furthermore it will always be a sine wave of the same amplitude and frequency, just with phase dependent on the axis angle. *3 dimensions of space + time
    1
  19. 6:04 OK. ;)
    1
  20. 5:17 From the Islamic Golden Age, when Europe was in its Dark Ages.
    1
  21. Something occurs to me: your derivation of the cubic formula requires some knowledge of differential calculus. But this was only developed by Leibnitz and Newton in the 17th century; it was not known in the 16h century. So how did Tartaglia and Del Ferro figure it out without calculus?
    1
  22. 👍 Amazing bit of work 👍 (I don’t know why YouTube has started duplicating my comment postings ... I only pressed “COMMENT” once each time ...)
    1