Hearted Youtube comments on Mathologer (@Mathologer) channel.

  1. I did wonder if it would appear in any "discrete math" or other "math for computing" contexts but my more advanced algorithms texts (where it might be found) are elsewhere. It is not in the DM book I have here.
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  2. 18:16 SPOILERS FOR ANSWER: (The method used) Start by placing 1 on the middle column and in the top row. Move: Place the next tile diagonally up 1 space and right 1 space. If the ‘move’ makes you go off the board, cycle back to the bottom row or to the left most column. (If you hit the corner do both) If the ‘move’ makes you end up on a space occupied by a tile placed previously, place the next tile the space directly below the previous one instead. (I.e. move 1 space down) This will ensure you fill the square with numbers in such a way that you will end up with a magic square.
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  3. Squeezing and stretching the snake, that sounds like lots of fun, and the result is quite beautiful indeed.
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  4. Thank you for educating us on Madhava...never taught in Indian school books..
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  5. CHALLENGES! 2:21 "Why is everyone using calculus - or being scared of it - when it's not required?" The calculus explanation is probably the most popular and obvious one. What can I say, calculus is robust. 15:49 "I hope you can forgive me for my little lie" Honestly, I thought something was off when you advertised the volume to be 8. I went through the calculus at the beginning of the video and got an answer of pi, checked wolfram and also got pi. But your reasons are perfectly valid, plus you gave a fix anyway to actually make the volume 8. You are forgiven. 18:06 "Let me know how this calculus-free exposition fares for you" Ties in REALLY WELL with your trilogy, and is a really nice way to finish off the series of this magical shape. Bonus As noted by someone in the comments, real world painters understand the amount of paint they use depends on how thick they apply it. One drop of paint is technically enough to cover the entire planet earth if it's spread thin enough, so it comes as no surprise that only 8 liters of paint can cover an infinite horn. Surface area and volume just work like that.
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  6. The most memorable is Kempners proof!
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  7. What An hour? hand hovers indecisively over play button and it's a masterclass? hand drifts away from the play button and I need to do my flute practice hand retreats to lap (oh very funny, plz don't go there) OTOH it's a video with a funny bald German in it hand approaches keyboard but there are probably no cats in it being cute hand falls to side crickets more crickets reciprocity prime what the? wat IS dat? Mathologer smiles impishly and wiggles the hook Command voice:" Lock all targets and fire at will! All ahead Warp 6! Take us in Mr Sulu!" Punches the big red button...
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  8. Is anyone going to download all the videos to some cloud, for a backup in case the channel will be taken down again? I'm planning to do it, but i'm not sure this is technically possible for one person.
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  9. Praise the lord, the legend lives on 🎉
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  10. Three minutes in, and Mathologer has already far exceeded the videos this video is about.
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  11. Exactly what I needed today EDIT: My favourite part was the no 9-s proof. It is just simply elegant.
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  12. Animated proofs should become routine in classrooms.
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  13. This video made me fall in love with Mathematics again. To know that people have been doing such amazing things from 1400s is absolutely humbling to me.
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  14. For the blackboard problem, it occured to me that 10²+11²+12²+13²+14²= 5 × 12² + 2 × 1² + 2 × 2² because the double products of (12+x)² and (12-x)² cancel. Knowing 12²=144, it is straightforward that 5 × 12² = 1440/2 = 720. The remaining squares sum up to 10 and we get 730, which is 365 × 2.
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  15. The similar triangle thing: if r1+r2+...+r5 = R (the decomposed red points as complex numbers add up to the red point in the starting pentagon) and b1+...+b5 = B (for the black points) you can just notice that the construction of any of these "ears" can be done by taking the vector from the r's to the b's (b_i - r_i) rotating and scaling it by some amount which is the same as multiplying by some complex number m, and then adding it back to the red position. So the coordinates of the new points is r_i + m(b_i - r_i), adding those up gives you r1+...+r5 + m(b1+...+b5 -r1-...-r5) = R+m(B-R) the same construction on the original pentagon.
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  16. 13:57 how many reg triangles and hexagons? minecrafters: YES
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  17. BUT big loans are socially* bad - so your point is moot. Big loans lead to kleptocratic Capitalism. A problem of scale - unbound credit. *?how much debt is sustainable in society?
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  18.  @jannegrey  One must remember that complex numbers are not complex as hard to understand but complex like an apartment complex eg. just two numbers joined together.
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  19. that is like saying 3 shouldn’t be prime because it is the only prime divisible by 3
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  20. So it’s like a Fourier analysis of a wave?
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  21. The determinant or closely relevant tricks are still intriguing topics nowadays. Leslie Valiant even introduced the name and opened a new subarea, “Holographic algorithms”, for these types of reductions (from seemingly irrelevant problems to linear algebraic ones).
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  22. What is interesting is that you can also turn any magic square into a new one by adding a non-zero integer constant to every square (the summations will change by the side length times the non-zero integer constant). Additionally there is probably some way to generate a new magic square by taking the modulus of every square (need to be careful about creating repeating numbers with certain values for the modulus. Edit: This actually might not be possible. I don’t have an example that it would work without causing a duplicate value).
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  23. 24:40 the sum of all the triangles that lower-approximate the blue areas is: 1/2*(1*(1 - 1/2) + 1*(1/2 - 1/3 )+ 1*(1/3 -... = = 1/2*(1 - 1/2 + 1/2 - 1/3 + 1/3 -... = 1/2*(1)= 1/2
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  24. I wouldn't say it was missed, but rather everyone who noticed it never bothered to write a paper on it. It's all part of the beautiful symmetry of mathematics in nature.
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  25. The best math comes from Side Projects. The things you think about when you should be doing something else.
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  26. Great video. Although wasn't this fraction in particular discovered by Laplace and proved by Jacobi. Of course, Ramanujan os a genius to have rediscovered it all by himself, but I was really hoping we'd get more about similar fractions. Digging deeper I found a book by S Khrushchev which discusses a whole theory of continued fractions like these along with great and largely unknown work done by Euler in this field. I think it can be found online as a pdf.
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  27. Yes mathologer video when i'm bored is the best of the best
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  28. The real question is: will a rubber band stretch the way it is presented?
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  29. The way Mathologer pronounces ramanujan makes me so happy
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  30. Youtube didn't show me this video until now and I'm annoyed so I'm commenting to try to convince the Almighty Algorithm to show it to everyone else.
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  31.  @mikemthify  He said "My original notes date from 1971." I don't know if that means he came up with the proof then but if he did he really would've been 19 and that just blows my mind.
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  32.  @ckq  Doesn't that mean it should be countable? 2ⁿ should be countable.
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  33. I didn't know that Homer Simpsons likes to teach math.
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  34. 3:20 minor formatting bug at the 53rd decimal place - the values are 2 and 1 but they're formatted as equal.
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  35. 20:16 This is brilliant! That's the very reason this theorem is about primes.
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  36. I dont even know math but your personality and enthusiasm has drawn me to watch
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  37. Thank you for all the effort you put into these videos. I very much enjoy the learning experience from watching this channel!
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  38. Thank you Burkard. Another fine video with lots of interesting and surprising twists and turns!
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  39. Great video! Another way I noticed of describing why that (1st power) integer sums pattern works is that the left hand side always begins with a square number n^2, and apart from that term, there are n terms on each side, with each of the terms on the right side each having a term on the left side which it is exactly n larger than. For example, with 9+10+11+12 = 13+14+15, the terms 13, 14, and 15 each have a term on the left hand side they are 3 larger than (10, 11, and 12) making the difference between those be 3 times 3, which equals the square number 9 on the left.
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  40. Very original video. I watch a ton of math edu content.. and I’ve never heard of math walls. Well done!
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  41. Thanks! Lovely reminder why I love elegant mathematics like this.
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  42. Here it is... Another interesting and deep connection between two (seems) "basic" things in Math. Really, this is all about: It's about deep connections, not just like "Did you know that a cup and a torus are equal, technically?". Math is beautiful with all its concepts and etc. what really amazes me are these connections. Man, It is such an art . It IS worth to spend the entirety of life with Math, really... No matter how it can be challenging sometimes.
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  43. I made it to the very end! Love the visual proof as always. My first guess at the second "what comes next" is 1, 3, 8, 21, 55, 144, just the Fib numbers.
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  44. "Of course, it would have been very hard to put into action in 1400 without a computer...." That's what graduate students are for!
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  45. It's actually the square root of 10, or about 3.162. It's the number whose logarithm to base 10 is exactly one half.
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  46. Love your work, you're rigorous and funny! Thank you. <3
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  47. Mandatory rewatch everyone! Do your thing, share with your friends who dont care about math!!
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  48. Great way to handle the found error. Might not be how the algorithm of Youtube wants and promotes it, but integrity in how you present information is one of the many reasons I'm a long time subscriber.
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  49. I wish I were a mathematician.
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  50. Animated version of the Pythagorean windmill proof: https://youtu.be/0VYYK-3tT1E
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