Hearted Youtube comments on Mathologer (@Mathologer) channel.

  1.  @VAXHeadroom  :)
    7
  2. Ah yes, I always like to express the polynomial 0*x as the product of all real numbers times a constant. Since f(x) = 0x has all zeros.
    7
  3. Iterative Turtles... Damn, so it is turtles all the way down.
    7
  4. Is there a geometric reason for the integral on your shirt?
    7
  5. 12:19 I was sure that this had to use integrals. e.g. the stretch factor of the rubber band when the number x is at the top of the rubber band is 1/x, so the distance from 1 to x around the circle must be the integral of 1/s ds from 1 to x, which is log(x). I guess I'm too grounded in my non-Mathologer ways to come up with this much cleaner proof!
    7
  6. This will come in useful in the gym later when I am scratching my head figuring out how to load up the barbell.
    7
  7. Personally I would argue that Tesla was more concerned with the behavior of the the numbers 3,6,9. For example the alternating pattern of the 3 and 6 or reflective of an alternating current pattern (the 3 being a trough and the 6 being a crest and alternating back and forth). The 9 always equates back to itself which is indicative of a cycle or the balance (or nullification) one gets when they combine the equal but opposite ends of a wave (i e crest/trough or in this case 3/6). In short, 3,6,9 just reflects the constant "movement" of the universe and everything else in nature. It's a WAVE in numeric form. Just my thoughts. Loved the video!
    7
  8. Not first
    7
  9. Me at 22:25 "This looks like a fun exercise." Half an hour of calculating generating functions later. "Well that's certainly not the Mathologer® way of doing things."
    7
  10. "Pretty obvious this pattern will continue forever." Fascinating how infinity is so intrinsically numerical...
    7
  11. These videos are so fun! Once I begin, I get so hooked that it's impossible for me to stop.
    7
  12. Definitely missed out on a great joke by calling them naught and nice numbers :') Great video once again, however. Merry Christmas to you and your team! :)
    7
  13. 12:58 At this point I thought "Why not just use triangles to do the argument?" so I've tried to do it, but then realised that the triangles, when you apply the rotation, actually grow in size rather than shrink, so the infinite descent argument won't work here. 21:00 I guess I'll prepare for that video more.
    7
  14. Damn Euler! The greatest mathematician of all time. True superhero.
    7
  15. yes please ❤️
    7
  16. This is the first Mathologer video I understood at one go. Keep it up professor 👍👍
    7
  17. The story of how Euler got into formulating quadratic reciprocity is fascinating. It's contained in "Primes of the form x^2+n*y^2" by David A. Cox. HIGHLY RECOMMENDED because it's an historical recount.
    7
  18. ​ @jannikheidemann3805  If you mean the United States, then yes, they teach Latin in many high schools, it's gaining in popularity, many Catholics study it independently to deepen their study of the faith, and many more people study the Latin roots of English in preparation for standardized tests like the SAT and GRE.
    7
  19. The most memorable part is the connection of the 'γ' and the log() function to the harmonic series! Really amazing!!
    7
  20. Top notch video! I was enthralled the entire way through it, and it was all easy to understand! Very well done!
    7
  21. I tried to prove all rational numbers have repeating decimal expansions before this video and found the proof down in it
    7
  22. Merry Christmas mathologer,thanks for our gift 🙂
    7
  23. When I was a kid, I learned the "casting out 9s" trick in some puzzle book (possibly by Jerome S. Meyer) my older brother had. I didn't learn why it worked until I read Martin Gardner's column about divisibility tests.
    7
  24. Dirichlet's approximation theorem states that any irrational number x is approximated well by infinitely many rational numbers p/q, in the sense that x differs from p/q by at most 1/q^2. This is proved by the pigeonhole principle!
    7
  25. Many civilizations discovered this triangle, India, China, Persia. If we have to hyphen the names of all the mathematicians who discovered it, it's gonna be a very long name. Also, In Persia, Omar Khayyam is not the one who discovered it. It's Al Karaji. Though it's true that later on, Khayyam continued Karaji's work on the triangle so successfully that it's called Khayyam's Triangle (مثلث خیام) in Iran
    7
  26. Man, Post's proof really was an amazing proof. That was one of those proofs that just makes me go "Wow!"
    7
  27. Despite the lockdown, the comforts I appreciate in life have really shown themselves to me and I feel grateful for what I have. These maths animations are among that!
    7
  28. This is great, I wish we would go even deeper into the maths
    7
  29. The thing is that, if the straight line assumption overlaps, then we always measure a bit more. Because, we know that the sum of the two sides of a triangle is always greater than the third one. If our assumption overlaps then it gradually leads to a fractal.
    7
  30.  @candiman4243  dangit I was gonna make that joke
    7
  31. Isn't it much simpler to see just the center of second coin if coin is outside than its center cover more distance than if it is inside 😃 we can also find the no of rotation by this 😌
    7
  32. Search again. Maybe we’ll get another video tomorrow!
    7
  33. I couldn't concentrate after chapter 3 because all I could think about was that amazing modified machine!
    7
  34. Matholgger just confirmed the Antarctic ice wall and flat earth. Wake up sheeple!
    7
  35. Matt Parker must have invented that anagram
    7
  36. Two years later this is still just as enjoyable and informative.
    7
  37. Most memorable: that cool proof that gamma < 1 by sliding all the blue regions into the unit square
    7
  38. The proof sketch was brillianty displayed. That "aha" moment you experience when it finally sinks in is priceless, almost addictive.
    7
  39. As a math teacher myself, I must say that this is beautifull and it's not very known even at graduate levels; I've loved this difference stuff for many years now and had very few people with whom share talks about it. Greetings from Argentina!
    7
  40.  @cliveso  Its an 1800-year-old problem for a pastoral society, it's not like you should be concerned with outside companies in the Bahamas or derivative securities. And optimal solution on R2 with the usual Euclidian metric it's not necessary and the optimal solution on all Rieman manifolds in R(n). The papers optimize for a set of reasonable conditions, more general than pastoral but not all possible solutions in all possible scenarios.
    7
  41. I’d love to hear aboeut Galois theory
    7
  42. Homeworks : 1) Considering a general nxn square, it is simplest to add the main diagonal, whose points stay in that diagonal. It becomes the middlemost row post transformation. Their points are (i,n-i) (1 at (0,0)) and the values are n+(n-1)*i for i from 0 to n-1. Adding, we get n^2 + n(n-1)^2 /2 = (n^3 +n)/2. For a 33x33, we get 17985.
    7
  43. I want that t-shirt in the shop!!
    7
  44. Definitely the most impressive part is the animated Kempner's proof, I've expected something extremely complicated and yet the whole thing was "nice and smooth".
    7
  45. I love this guy! Keep 'em coming!
    7
  46. This is the best possible christmas gift 😁😁 Thank you MATHOLOGER Merry Christmas ❤️❤️
    7
  47. I wonder if there are any similar fractal-like paradoxes? ("volume" slightly less than 3 dimensional finite, yet infinite "surface area" slightly larger than 2 dimensional? Any trade-offs here as the two dimensions approach each other?) Hmm, something for me to ponder!
    7
  48. I won't be surprised if this video would suddenly get dislike bombed by rabid fanboys with in a week. Some people really don't like when they're told that their branch of woo isn't special.
    7
  49. Can you do one on why the platonic solids fit so nicely inside each other?
    7
  50. New IAU-approved prime definition: 1. must have only 2 indivisible factors (1 and itself) 2. must be odd 3. must be large enough to have cleared its orbit of all other integers.
    7