Hearted Youtube comments on Mathologer (@Mathologer) channel.

  1. 21:30 As soon as you started talking about magic, I knew recursion would be involved. Recursion is the basis of all reality, my friends.
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  2. Weird curve's diameter= L1+L2+L3 which is a chord of Conway's circle not containing its center < diameter of Conway's circle. BTW, (Conway's Radius)^2 = r^2 + p^2, here r is the incenter's radius and p is both the triangle's semiperimeter and the weird curve's "radius" (there's no center). You can get r = H/p, using Heron's Formula (H)
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  3. The world is always a bit better with a video from the great Mathologer. I am glad you put this together, thank you Mathologer!
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  4. The solution to the puzzle at the end is easy, you can consider scanning across 2-wide columns and 2-high rows. Each time you move the square, you know the colors in the newly covered squares have to be exactly the ones as just left. This gives us half the solution for free, since it it implies corners along an edge must be different, since the rows and columns have different parity. It's not a full solution because it doesn't exclude the case where a color is the same on one corner and the one opposite it. You can use an inductive argument to prove this. If the opposite corners really have the same color, then that forces the inner cell of the 2x2 squares at the other corners to have that color (by similar row/column parity reasoning). This means we have a (N-2)x(N-2) square with same colored opposite corners. In the 2x2 case, this is excluded by the puzzle's rules. Thus we can form an inductive argument, (1) a 2x2 square trivially cannot have the same color on opposite corners, (2) a (N+2)x(N+2) square cannot have opposite corners with the same color, as that would require the NxN square inside it to have opposite corners with the same color. Note that this only applies to grids of even sizes. Although I think that proves more than you wanted now that I rewatch that. I'm still confident in my solution and that it holds even in cases like 6x6. Here's a diagram to help visualize the tricky case for 6x6: a_?_?_ __?_a? ??a___ ___a?? ?a_?__ _?_?_a
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  5. Yes, you are right. My intuition was wrong. I love how these videos get people talking—any ideas on getting 15-16 year olds talking like this?
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  6. I put on the captions for my deaf mother and we both appreciate not only the effort you put into them but also the smilies :)
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  7. Love me some mathologer masterclasses... still waiting on that Kurosawa length Galois theory video :)
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  8. "Coins may become an endangered species" Or better yet, endangered specie!
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  9. The column sum of the 33 square is 17985. It's just the number of squares (1089) into Gauss' sum formula n*(n+1)/2 over the number of columns (or equivalently rows).
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  10. I am so glad that you are still around!
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  11. 17:30 Just remember that the triangle can be thought of as a half of a parallelogram of sidelengths A and B.
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  12. this is a great topic for an undergrad first year calculus class.
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  13. What perfect timing! I just remembered these claims about Vortex Math and mentioned the explanations of their patterns in the comments of a math meme about how 9 is only special due to the decimal system. :)
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  14. I do NOT remember it being taught in my school in England in the 1960s. I do remember coming across it in my mothers school textbooks - but not with Heron's name attached. Always thought it was fabulous - particularly like the way it gives a zero if S is any one of A, B or C which corresponds to the triangle collapsing into a line.
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  15. Bioware put this in KotOR, and I had to memorize this thankfully simple recipe because I did multiple playthroughs. Years later, they put it in Mass Effect 1 and I still remembered it. And years later I saw this video and still remembered it. Stuff you do repeatedly as a kid really sticks with you, huh?
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  16. I actually really enjoyed the blinking eyes. Well done!
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  17. Ah that bug explanation is lovely! Wish I’d given it more thought myself first haha.
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  18. first
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  19. Great, as always! Loved the animations of Thompson and Leibnitz and the metal soundtrack of the end (though I've always been a fan of the usual wistful and nostalgic guitar theme)--it was distracting, but worth the distraction!
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  20. When you laugh it very hard to differentiate you from a James Bond movie villain.
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  21. it’s amazing to also know that the flavors of derivatives and integrals were already discovered by Indian mathematicians before Newton ❤
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  22. My favourite Mathologer video thus far. Props to Archimedes et al.
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  23. Prof C.K Raju [INDIA], also complied with previous old mathematician work, you can also see that. thank you for the amazing video.
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  24. So he is a doctor and a plumber....and also a mathematician 😱
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  25. Thank you for this new, great Mathologer video! I am really enjoying this long video about that absolutely interesting topic! 😄
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  26. This was the best of your videos. I am a PhD student of math, and today I learned something new which I have to look into much more. Definitely more of this please. Complicated math is my bread and butter and you are one of the few youtubers who dares to go into the details. The length of the video was absolutely appropriate.
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  27. I have a different perspective on "the king's method". When I went about proving the method, I looked at the form the columbs take when we unwind the magic square back to the lunch box formation. Under that perspective each columb corresponds to two diagonals with a combined leangth equal to that of the columb. Than the key to proving the method is to show that when shifting from a columb to its' adjacent, the sum over one of the corresponding diagonals increase by exactly as much as the sum over the other will decrease.
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  28. This is a masterpiece!
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  29. I had always thought of myself as a mathologerist, but now I see that I was always a mathologerer.
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  30. On Ramanujan's channel this video is 20 seconds long and the explanation consists of him saying "I saw that this identity must be true"
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  31. Exciting, awesome video. Absolutely amazing.
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  32. I am an engineer, and I have to say that the video is crystal clear. I really wish I had such clear presentation back in the days!
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  33. I often wondered why you didn't have a patreon and ads on your videos. Please, monetize NOW (and do employ someone for the editing, etc.)
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  34. Amazing content, as always :)
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  35. Honestly it blows my mind when I see these mathematicians from India generated some of the most popular integrations, limits and whatnot with sheer simplicity yet mysteriously and seamlessly embedded them either in a poem or a mantra or a prose so not only the willing one is able to synthesize the literature written but able to practically implement the math encrypted in it. Even more interesting is that these mathematicians always dedicated their discoveries to God and let the discovery have an open access for all irrespective of their background without claiming to be the founder of the said discovery; precisely why I am convinced to believe why several of their discoveries that we today are studying/ using don't bear their names.
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  36. This was super enjoyable. Loved the bit of history along with a fantastically clear explanation with great graphics. Just great fun.
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  37. 25:02 small typing mistake here inside the third pair of parethsesis, you wrote "A+B+D-B" instead of "A+C+D-B"
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  38. 3:40 After you had got to the line of 1's I immediately got to my mind what Babbage was trying to do with his machine. Automate the process of calculating differences. So this is calculus because calculus is the mathematics of differences.
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  39. Thanks for your videos.
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  40. The Talmud is in some ways more a legalist text than a religious text. It's basically a collection of legal opinions, and it's also full of dissenting opinions.
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  41. 42:49 Is that the same Markus Persson that created Minecraft?
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  42. It works if the surface "moves outward at the same speed" everywhere when the parameter is increased. So the perpendicular thickness of the shell (the dV) is equal everywhere (the dr). For instance, the area of an ellipsoid is NOT the derivative of its volume (for common parametrizations). Even simpler, it doesn't work for non-regular polyhedra. Like, the volume of a pyramid with square base with side x as well as height x equals ⅓x³, but its area is (1+√5)x²...
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  43. 0:35 "on the look-out for the mathematical soul of things". Haha - nice shout out to Shylock ("not on your sole, but on your soul...").
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  44. 7:39 the coloring proof I suppose. The static picture that you can look at and check over feels more comforting somehow.
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  45. Now we are just waiting for Mathologer to compare the Laplace transform to the Z-transform in a simple way :)
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  46. my comment is 1st your video has made me felt proud the most ❤️💕 india ❤❤
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  47. For many years, and from the first time I knew that I should support this wonderful math channel!, I really feel happy that you're still going forward!
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  48. Yeah the recursion for the 3 and 9 divisibility rules was something I'm not sure was taught because it seemed so obvious to me I think they don't mention the remainder thing because they don't really care about remainders
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  49. Here when there's less than 1000 views! Woohoo! The last time I was this early, I didn't exist
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  50. Another great video as usual, I will definitely revisit this one after doing more studies. I just love the attitude towards math you have, and that you poke fun at those "intelligence tests". Those tests are so easy if you just know the trick, it's hardly an 'intelligence' test as it is a knowledge test at that point. Maybe very clever people might come up with the solution with no prior knowledge though.
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