Hearted Youtube comments on Mathologer (@Mathologer) channel.

  1. The GOAT has returned
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  2. Welcome back! So happy to see everything back to normal!
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  3. Nice π-zza shirt
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  4. Yay! I think I need to invest in Mathologer T-Shirts!
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  5. The tiling of 2 by grids is Fibonacci series with first term 1 and second term 2
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  6. New subscriber sir
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  7.  @Mathologer  A cool thing one can do on an E-6B, is "enter" winds aloft for several altitudes simultaneously (direction and speed), thus one can optimally choose the altitude of flight for time and/or fuel. In a mainly head/tailwind case, isn't worth the effort (unless the winds are very strong), but when crosswind, then there may be surprising options.... (entry is a pencil mark on the vector plate).
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  8. It's taught very carefully in India, but i doubt how many students actually care about it.
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  9. I think this video shows why math education channels like Mathologer are so important; a simple, easy to explain proof didn't exist, so you made it! Maybe it isn't the most rigorous, but being forced into the visual medium instead of a dry, mathematical paper makes things WAY more understandable.
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  10. This has some fascinating connections to a type of random number generator called an MLCG, which is a special case of the commonly used LCG.
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  11. 13:43 the numerators follow the pattern a1=1, a2=3, a(n)=2*a(n-1)+a(n-2)
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  12. With the Magic Cube 4D app sitting in a dark, forgotten directory for years, this video gave me the tools to solve it in a single day. Thank you. Your other videos are also fantastic, you explain things very well and have great charisma. Keep it up!
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  13. I don't remember which proof I saw first but a few weeks ago I wanted to show a proof to one of my kids and realized I forgot all the proofs I had learned in school. The second (algebraic rearrangement) was the one I worked out first.
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  14. My background in maths: two years of an undegraduate degree in theoretical physics before dropping out due to ill-health, then haven't really done any formal maths for the ~15 years since. My experience with this video: I was following everything fine up to the Bernoulli numbers; from that point on I was following enough of what was happening to still find it interesting and enjoyable to watch, but I'd have to go back and rewatch -- probably with multiple pauses -- if I wanted to be able to say that I truly understood it all.
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  15. Finnish engineer student here. Heron's formula is in our textbook and might have been mentioned like once during a lecture. But we mainly used laws of sine and cosine to solve triangles.
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  16. Is it weird that as a break from studing lineal algebra im watching a mathologer's video? xD
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  17. Most Memorable : Every seconds of this video. I couldn't choose a single thing. I am sure that this is the best video I have ever watched in my life related to anything. Thank you so much Mathologer.
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  18. A great way to look at familiar stuff. Top 5 Mathologer video of all time.
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  19. I used to solve towers of hanoi on fights because I had no internet. Solving the 10-peg version with 1023 moves must've been one of the proudest moments in my life :D Edit: huh, I didn't know the "smallest disk" trick explained at 12:18. I just tried to follow the recursive algorithm in my head. Way to trivialize my life's achievment, Mathologer! /s
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  20. I find it astonishing how numbers align so well. Much better than stars. Beautiful video as always.
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  21. A mathologer video with less than 50 comments? That must be brand new. Must watch now!!!
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  22. Observations: If one circle has a radius of A and the other has a radius of B, and the radius-B circle revolves around the radius-A circle, then there are two equations depending on if the revolution is internal or external. The tilt of the radius-B circle per revolution is (A - B) ÷ B × 360° if the revolutions are internal. If the number of revolutions is external, then that value is (A + B) ÷ B × 360°. The easiest explanation for these equations is that the tilt of a circle is always 360° times the distance the origin of the circle travels divided by its circumference. The radius can also be considered negative for internal revolutions.
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  23. Thanks for recognizing Indian Mathematician Madhava for his work on Calculus and infinite series relating to Pi. More than the credit, I am interested in bringing in awareness among talented Indian youth towards Maths which is currently more influenced by cash-generating Wall-street jobs and related courses.
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  24. Is it a known fact that you can get from any domino tiling to any other tiling by rotating 2x2 squares? Seems true for non-hole boards...
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  25. Neat proof of an amazing result! I'll have to watch that show because it sounds like the best use of math in a film / tv show ever. Also, nice pi shirt!
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  26.  @conanedojawa4538  No because it is a root of polynomial equation r^3-r^2-2r+1=0
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  27. Reve's table of Cheeses is an extract from a leaning Pascal's Triangle
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  28. was that an arctic cardioid at the end? how... cold-hearted of you :P
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  29. 2:10 I saw the sqrt(2) version that uses the hypotenuse of a triangle with the other sides equal to one. Happy holidays!!!
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  30. My first thought with seeing this was a way of defining a Dual of a triangle (up to scaling), following up with some theorems saying "A triangle has property X iff its dual has property Y". Time to explore.
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  31. I've just discovered there's no greater way to start a Christmas day than with a Mathologer video x
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  32. only comments after 36 minutes are valid
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  33. This portrait of Madhava looks suspiciously similar to a certain Mathologer...
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  34. Greetings from Czech Republic and Thank You for educating me about the achievement of my fellow countryman I was not aware of.
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  35. I'm going to tile my floor with randomly generated aztec square arctic circles, in shades of grey.
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  36. I see Mathologer's new upload. I just literally drop anything else I do, and watch. Cat video after this, maybe? :)
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  37. Would the maximum number of moves to turn all 10 cards over be 55? By flipping the digits furthest to the right on every move, you decrease the binary value by the smallest amount, and it would take 1 move for the first bit, 2 moves for the second bit, all the way until 10 moves for the 10th bit. So 1+2+3+...+10 = 55?
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  38. THAT is a COOL STORY!! - WOW!! (damn... I love the comments on these videos!)
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  39.  @Mathologer  Some of us know about him, but I agree, the guy was a legend and deserves much more attention. India's advancements in Maths and Sciences were severly affected in the last millenia as Indians had to deal with islamic invasions and subsequently european invasions.
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  40. I did a bit of trigonometry to express the six angles with the coloured dots in terms of the angles of the given triangle. Here's what I figured out. (I'm sure this is known to the triangle experts.) With the usual notation, let's call A, B, C the points of the triangle, a, b, c the edges and alf, bet, gam the angles. The median through A divides alf into the angles alf_b and alf_c (to the side of the edges b and c respectively). Similarly, bet=bet_c+bet_a and gam=gam_a+gam_b. With this, one gets: cot alf_b = 2 cot alf + cot gam, cot alf_c = 2 cot alf + cot bet and two similar pairs of equations. (The proof uses the law of sines and the addition formula for cot.) Btw., it can be checked that cot(alf_b+alf_c)=cot(alf). Now the folded triangle has angles alf_F = bet_a + gam_a, bet_F = gam_b + alf_b, gam_F = alf_c + bet_c, and one obtains cot alf_F=(-cot alf + 2 cot bet + 2 cot gam)/3 and two similar expressions for cot bet_F and cot gam_F, i.e. a linear relation between the cotangents of the angles! So, if one forms a 3-vector from the cotangents of the angles, then the folding operation from the video is the multiplication of this vector with the 3×3-matrix M which has -1/3 on the diagonal and +2/3 in all other entries. This matrix satisfies M^2=1, reflecting the fact that folding twice reproduces the triangle up to size.
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  41. Does the distribution of numbers around this wheel correspond to Benford's law about the distribution of the first digit of random values?
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  42. Your animations were amazing, I would have never been able to visualize this without your excellent animations. I was truly impressed, I learned a lot thank you!
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  43. Got to the very end and I'm wondering if this could be used to pay taxes more fairly. For that I would change how we see the creditors as they are now debtors and so, the one with more to gain from the budget (the richest) would be the one to pay first, then the second richest up until the poorest, then when the poorest are maxed paying, then the second poorest... And finally the richest. We would be taking the inverted picture of the areas and still be using communicating vessels, having the ones with more to gain paying more at the beginning and at the end and also having the ones less to gain in the middle, paying all and maxing out first but when all others have equalised with them already.
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  44. After preparing for competitive math Olympiads i hated geometry, this video has shown me the true light of how beautiful it is.
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  45. This is one of the clearest mathematical expositions I have ever heard.
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  46. Mathologer love ❤ fav channel
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  47. No. You must make stokes theoreom videos
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  48. Damn, this is one thing I've know about for a while but no-one else seemed to know about, so thank you for showing this to the world.
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  49. You left out the fact that the Hanoi constant 466/885 gives the average distance between any two points in a sirpinski triangle with a side length 1
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  50. Combo Class has a video as well on the {2,2}, {1,2,3}, {1,1,2,4}, ... infinite family. But they're very different and complement each other nicely.
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