Hearted Youtube comments on Mathologer (@Mathologer) channel.

  1. Youtube tried to give back the IQ points I have lost watching Schiff argueing for impeachment by recommending this video.
    8
  2. @mikemthify Roger Heath-Brown was 19 in 1971. Could you post some sources?
    8
  3. Beautiful theorems. Elegant presentation. Bravo!
    8
  4. I wonder : if one were to 3D print these pseudo3d timings into actual 3D shapes, would the « arctic circle » turn into an arctic section of a sphere of sorts? What about matching pairs? And what about higher dimensional tilings ?
    8
  5. A slight alteration to the overshoot/undershoot algorithm I believe already gives you uncountable infinite ways of doing it. The alteration is that you can overshoot and undershoot by as many terms as you please, and you can choose a different number each time. This still works because the positive and negative terms sum to infinity. Because you’re choosing a natural number by which to overshoot/undershoot at each stage, the number of choices you can make is equal to the cardinality of the reals (because each choice corresponds to a sequence of natural numbers) which is uncountable.
    8
  6. Would it make sense to get a mathologer video someday on the continuum hypothesis? I know that it's undecidable but I have no idea why. If there were a way of making that fact familiar and intuitive, that'd be a big deal to at least a very countably finite subset of your audience
    8
  7. Fun fact: if you have a circular slide rule as an avatar, there is a lot of questions like "What a strange scale on this stopwatch?"
    8
  8. I work at a bank and one flaw I can see with this method is that when providing a loan there is no transparency as to how much the bank can expect to recover upon non-payment of the loan. This is an important variable for banks and is why they can provide mortgages with relatively reasonable rates, since they receive (a portion of) the mortgaged property upon default of the home owner. If I provide a loan to a company, I can estimate from financial records an expected total recovery amount, but I would typically not know how many other creditors there are.
    8
  9. To answer your question about other countries (although you might already know this): Suggesting to include something like Heron's formula into the mathematics curriculum in Germany would make the other commission members look at you as if you had told them to leave the building because a marsian space ship has landed on the roof.
    8
  10. Very nice theorem! This folding process gives some sort of "sides-medians duality": -The sides of the folded triangle are each 2/3 the length of the corresponding medians of the original triangle; -The medians of the folded triangle are each 1/2 the length of the sides of the original triangle. This proves the 1-time-folded triangle is in general not similar to the original one, but the 2-times-folded one is similar to the original one, with a lengths ratio of (2/3)*(1/2)=1/3.
    8
  11. When I saw the penrose tiling at the end I gasped! So interesting as always ❤
    8
  12. Try to find a mathematical branch where you don't find a speck of either Euler's it Gauss' contribution. I'll wait.
    8
  13. Now that is an interesting way to deal with fairness. Impressive.
    8
  14. The little German that I know, I learnt from a Dick Smith Electronics print Ad from decades ago. It is how to complain about rip off retail store prices: "Gross schoppendollarpreiss, upderjumpersticken!!"
    8
  15. I liked the crazy optimal overhang tower the most. Didn’t expect that at all.
    8
  16.  @Mathologer  Oct 1973 Scientific American, reprinted in "Knotted Doughnuts and Other Mathematical Entertainments".
    8
  17. I'm so impressed by the way you make difficult mathematics easy to understand. Thanks for inspiring me to be a better teacher :)
    8
  18. You are too pretty
    8
  19. Fantastic lecture. Btw no equilateral triangle actually follows quite quickly from picks theorem & area =(1/2)s^2sin(60)
    8
  20. I get the same, n²(n²-1)/12
    8
  21. Hello there
    8
  22. 24:13 The location of the center of Feuerbach circle for the 3-4-5 triangle is on the same horizontal line as the incircle, therefore the outlined procedure will produce a degenerate triangle (a line).
    8
  23. Mr Mathologer, do you know any visual proof of Pick's theorem? Using that, it's easy to prove that no equilateral triangle fits into a square grid: Let's suppose that one of these triangles exists. By Pick's theorem, the area of any polygon with its vertices on grid points must be n/2 for some integer n. (For the equilateral triangle, this is also easy to see by inscribing the triangle into a rectangle and then subtracting three right triangles with integer legs.) But if we name "s" the side of the equilateral triangle, then its area is (√3/4)s². As s² is integer (because it's the Euclidean distance between two grid points), and using the fact we previously saw, then (√3/4)s²=n/2, meaning that √3 is rational. As always, thanks for your amazing videos!
    8
  24. So, there is no way to advance 5 steps in in this solitaire army game. And there is also no solution to a general 5-degree polynomial involving only basic arithmetic operations and radicals. Coincidence? I don't think so ....
    8
  25. As always T-shirt on point
    8
  26. I have loved each depth of unveiling the mathematical concepts ❤ Thank you, mathologer, for building concepts deeply always😊
    8
  27. 10:43 The number of rotations equals the distance between the center points between both coins divided by the radius of the rotating coin.
    8
  28. Hello early gang!
    8
  29. I am very happy that Your channel continues to work. Your wonderful deeds, o Lord.🙊🙃
    8
  30. I am so grateful to you sir, for giving the credit of discovering Calculus back to Medivieal Indian Mathematician from that of Newton ... Kindly search for more Mathematicians like Bhaskaracharya and you'll be amazed to discover most of the discoveries of Maths as modern world know of ... Thanks once Again sir
    8
  31. Love your channel =) one of the best math channels
    8
  32. you have blown my mind once again. absolutely loved this video, and the animation was amazing! amazing work!
    8
  33.  @Filipnalepa  the banana has a concave shape. You might think that if you were dealing with a convex shape your intuition would have been correct. Unfortunately, it is not the case. However, any line that goes through the center of the mass of a shape, cuts it in two halves that have equal, but oppositely signed "first moments of area". You see, the area of a shape is the integral of (dA). The first moment is the integral of (x dA), where x is the location vector of the infinitesimal area element dA. You can imagine the area as the "zeroth moment" of area. Your intuition told you that the halves had equal zeroth moments, while the reality is they have equal but opposite first moments.
    8
  34. I wish the video had been 10 minutes longer with just a tiny bit less appealing to the gods. Thanks for this. (High school math teacher / enthusiast)
    8
  35. Fermat was where "The proof is left as an exercise" started.
    8
  36. Ah yes, I gave a talk to the math club at my school demonstrating the difference calculus applied first to polygonal numbers, then I revisited the triangular case and derived the tetrahedral formula, ending with a pascal triangle surprise. The interplay between the discrete and continuous is, in my opinion, an understated mathematical motif which I felt the need to highlight in my one and only pedegological presentation.
    8
  37. 13:19 That is an easy one. For any n number of disks, you just change the direction depending if n is even or odd. N == odd -> direction == clockwise. And N == even -> direction == anti-clockwise. ;)
    8
  38. 14:25 I think it's no coincidence that the opposite side of 1 (half a circle) is about 3.14, which is pretty much pi.
    8
  39. It's no coincidence that it is the sqrt(10). The distance is log(10)/2, (let's say natural log), and so to get the units we do exp(log(10)/2)) which is sqrt(10).
    8
  40. I love the little giggles. Could be a bady in a bond movie
    8
  41. Mathologer Are in Melbourne. ?? From a Melbournian
    8
  42. I love it. Congratulations! Euler is a spectacular mathematician, even today.
    8
  43. I recently solved that problem on codewars and came up with the 10 rule myself (looking at the results of many different triangles). Helped me solve it fast enough
    8
  44. Mathologer videos are always such an inspiration to me. I'm no mathematician, but I enjoy a bit of mathematical dabbling. Most of my exploration is what might be called empirical mathematics. In short, I look for patterns without bothering too much about proofs. To test my pattern-finding ability, I paused the video at 29:01, to see whether I could identify the next few members of the family. I got the following: 9² + 40² = 41²; 11² + 60² = 61²; 13² = 84² = 85²; 15² + 112² = 113²; 17² + 144² = 145². The general pattern could be expressed as (2n + 1)² + (2(n² + n))² = (2(n² + n) + 1)², where n is a natural number. The pattern for the family shown at 30:12 was even easier to identify. The next few members were: 63² + 16² = 65²; 99² + 20² = 101²; 143² + 24² = 145²; 195² + 28² = 197². The general pattern for this could be expressed as (4n² − 1)² + (4n)² = (4n² + 1)², where n is a natural number.
    8
  45. I honestly don't know any mathematicians who aren't willing to acknowledge mistakes. I mean it's always hard but it's part of what I like about math. I mean if you aren't making mistakes you aren't working on hard enough material and the nice thing about math is you can't just pretend that your mistake was correct.
    8
  46. But what if we take Input = {n^k} for any k > 2 ?! If you post the answer before me, you get a cookie.
    8
  47. That's true, the primes page on Wikipedia doesn't exist in any other language yet.
    8
  48. ​ @zlodevil426 "you only say the food is disgusting because it's made out of trash"
    8
  49. RIP Graham, a true GOAT 🐐🐐
    8
  50. Loved the video! Definitely really easy to understand compared to other Master Class videos. I think it helped that it was very interesting so taking it one step at a time didn't cause me to lose interest
    8