Hearted Youtube comments on Mathologer (@Mathologer) channel.

  1. Knowing there is some trick to guessing quickly I looked back at the examples. I noticed that the top left and right corners added to the bottom one in each. Let's see if that hypothesis is right!
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  2. We can rewrite the correction 1/( N + 1/( 4N + 4/N) ) as 1/N * 1/( 1 + 1 / ( 4N² + 4) ) which, using 1/(1+eps) = 1-eps, approximates as 1/N * (1 - 1 / ( 4N² + 4 ) ) = 1/N - 1/(4N³ + 4N) which once more gives 1/N - 1/(4N³) * 1/(1+1/N²) which approximates as 1/N - 1/(4N³) * (1-1/N²) = 1/N - 1/(4N³) + 1/(4N⁵) So the errors when N equals a million occur near the 6th (N), 18th (N³) and 30th (N⁵) position, explaining the sizes of the series of correct digits even a bit better. (This works because the error in 1/(1+eps) = 1-eps is also of order eps³, hence why the coefficient of the 1/N⁵ term seems wrong compared to the video; a better approximation would account for that term, but I didn't want to complicate things too much...)
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  3. if you can put up some videos for group theory,then probably i would be the happiest person in the world.
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  4. Crazy day! I literally told my friend about the Bernoulli Numbers (and finding them using Pascals Triangle) and the Euler-Maclaurin Formula today (we found the formula for summing 66*x^6 to the n'th term) Approximations are really my thing I'm doing with mathematics lately, and I've used the Euler-Maclaurin formula for approximating the Zeta-function. I have a whole spreadsheet with approximation of special functions. (I also fell a mathematical tear when you mentioned the Stirling Approximation as it in my opinion is the most beautiful thing in mathematics even surpassing Pythagoras and Euler's Identity, hoping for a video on it one day) Education is High School, so I get most of your videos (but the videos on transcendental numbers I still struggle on), due to my previous workings with the Euler-Maclaurin Formula I understood this video really well, but for someone who's not heard about Bernoulli Numbers and the Euler-Maclaurin formula before, it might be difficult. Looking very much forward to more videos on this (and that Stirling's Approximation video!)
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  5. I just watched it for the second time today. It's even better the second time around. The length actually adds to the clarity because it attacks the problem in multiple ways.
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  6. I understand every point, it was very interesting.. Thank you Sir..
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  7. Absolutely amazing! Don't worry about length, this was too beautiful not to share!!
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  8. Mathologer videos slowly becoming true epics in mathematics
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  9. Thank you for presenting this. Haven’t had a math class in more than 40 years but I did have formal logic which helped a bit when following this video. If I had seen this in high school I might have had a whole different career path.
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  10. Watched 28 minutes video, but only thought: "why so short? I wanted more pi formulas!"
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  11. Phew! Got through it but need to rewatch how those crazy calculations in a pre PC era where done. My background is in computer science.
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  12. Great video as always! I think it’d be really cool if you did a video on Minkowski’s Lemma and you could use it to prove the Fermat’s Christmas Theorem. The proof is relatively simple, but I didn’t see this until Uni
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  13. To infinity and beyond... talk about tilting at windmills.
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  14. This is honestly the best video on magic squares on YouTube & the best comprehensible video on the topic I've ever seen. SUPER! B)
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  15. My dad gave me his circular slide rule that he got back when he was in university. It was produced in 1957. Really cool for me to have and play with, but I love the rubber band explanation!
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  16. ​@Mathologer I found it uncanny but still pretty cool
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  17. how you develop 'wonder' thing? I am not wondering at anything
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  18. After seeing this proof it looks like that this theorem could have been put in an Olympiad problem also
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  19. Hope this is good
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  20. "Why halfen the container size?" Simply to make the model's numbers (containers) match the Talmudic numbers. In this step, Mathologer is just exploring how water containers could be used to try model the Talmudic problem. Again, the original problem is actually to try to figure out what fairness-reasoning the Talmud is using; but the first step is just to try some model that produces the same numbers, and then to look at extending/modifying the model to see if it gives insight into the original problem's reasoning.
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  21. In other words, yes, seven million people CAN be wrong. But I already knew that. And I really, really dislike Tesla-groupies.
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  22. Australian
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  23. Noice
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  24. I am studying math in university right now, and I am not put off by such a long video. I had to split it up into chunks for when I had time, but it was intriguing, so obviously I watched it all the way through, and if you continue to produce videos like this, I would watch it even if it was 2 hours.
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  25. To me the fact that you can get from one convergent to the next is amazing. At first it looks like putting one more coefficient means you need to calculate the fraction again from scratch. But the picture makes the quick way so obvious!
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  26. 44:25 did everyone REALLY miss the fact that 'Markus Persson' AKA NOTCH! watches mathologer!!
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  27. I came up with a poem of my own for the cubic formula: x^3 + n*x = m x = cbrt(m/2 + sqrt(D)) + cbrt(m/2 - sqrt(D)) D = (m/2)^2 + (n/3)^3 When x cubed and x times n, Are added and equal to m. The values of x, The goals of our quest, Here's how to calculate them. Cube roots to add, Square roots they had, Both of a term we'll call D. Square half of m, Cube third of n, Add together and see. Half of m, adds to the root, First with a sign of plus. Its little brother, Is just like the other, Except with a sign of minus. Cube rooting time, of both the brothers, Add up the roots with glee. We found our first x, But where is the next? I know there have to be three. With help from DeMoivre, Who's theorem, we love ya, There's cube roots all over the plane Yes, they're complex, But do not perplex, A new kind of numbers we gain.
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  28. And thank you so much for getting another video out before Christmas. Especially one with things to ponder over the break!
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  29. Now you've set yourself up to mathologerize the representation theory of Sn, and I can't wait for it.
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  30. Funny thing, in the film clip the proof relies on the 'fact' that starting with a positive integer and reducing its value must eventually result in a negative number, but in this problem the number goes to zero in finitely many steps and never becomes negative.
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  31. This is the reason why I mayored in math: to watch Mathologer master classes from start to finish
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  32. yes, very special! I wondered about the Chinese (or Japanese, as it turns out) flavoured music, but I guess it was suggested by the sinuous line of the baggage carousel. I was really skeptical about the preservation of the area through the meridional lay-down, but the travelling circle argument convinced me. So much to think about in this video!
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  33. I am very very fascinated by 1) How hardworking you are with all these presentations 2) How kind, positive and interested in math you are. It's perfect that you make these videos, it literally makes me much happier because i fall in love with math more and more. P. S. Sorry for my english, it's not my language.
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  34. @Vihart will love this episode :)
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  35. I love the no comment animation at the beginning. Well paced to be able to capture the sequence. Maybe do some more of this conzent. Not for shorts though as there's not enpugh time.
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  36. I think it's also nice to mention two certain patterns cos'x = -sinx sin'x = cosx Buuuut what if it's like cos'x = sin(-x) sin'x = cos(-x) sin(-x) = -sinx cos(-x) = cos x Pretty neat. And the other is the derivative of a constant: C' = (Cx^0)' = C(x^0)' = C * 0 * x^-1 = 0 Which also shows that there is no x^n that results in x^-1, but that function must have an integral, right? And it's the only one that connects to lnx, as ln'x = 1/x = x^-1
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  37. He caved in and gave us the clickbait we deserved 🗣️🗣️🗣️📣📣📣
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  38. In all seriousness: yes, calculus is easy. Or at least not as hard as most people think. But you need to approach it like you did here: by discussing a real-world case you already know about. I learned calculus exactly like that. In physics class, not math class. And I suspect I am not the only one.
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  39. I will always have a soft spot for the Wolfram spiky
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  40. Ahhh endlich!
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  41. Yeah it just got recommended even though I've been waiting for this to be done on a big math channel for a while now
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  42. yes, we were actually taught the "digital sum is the remainder" thing, our school system here loves to emphasis on the little tips and tricks instead of heart of the matter, take that as a negative or positive, up to you
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  43. For each even n (you mention n=4), you have a round with 'flat ears' (180 degrees). Instead of looking at the 'tips of the ears' for constructing a new n-gon, there is anothe way of looking at it: in each round add regular n-gons to all sides and construct the new n-gon by connecting the midpoints of these added regular n-gons. The difference in the rounds (the different degrees in the 'ear wording') is by aligning not two consecutive vertices of the regular n-gons, but such that k vertices ly on one side and n-2-k on the other side, for k=0, 1, ..., n-3. So it is like every round of constructing a new n-gon is by adding regular n-gons 'sunken one vertex more than previous round'. (And indeed the rounds can be permuted.) You can see this visualised in the Geogebra application found at Geogebra ... /classic/sdftbe2y. So there are two equivalent formulations of the Petr-Douglas-Neumann theorem: - using tips of triangles (ears) with different angles per round; or - using centers of regular n-gons 'sinking' through the edges per round. The intriguing idea is that Napoleon's theorem uses the second formulation and Van Auble's theorem uses the second formulation only for the 'first round'.
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  44. 6:22 Remove (0, 1) and (1, 0) (=> same color) and 2 others of the opposite color anywhere except the corner (0, 0). That's 2 black + 2 green removed and you won't be able to tile the corner (0, 0) :-)
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  45. Can you please make a vedio on the very less known, but very interesting kaprekar's constant After seeing this vedio i had a feeling that it can be proved using the same pegion hole principle
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  46. The videos are always worth the wait! ❤❤❤
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  47. The trick I always used for the tower of Hanoi is based on odd or even quantity of discs. If you have an odd number of discs then the first move will be to the target tower. If you have an even number, then your first move will be to the other empty tower.
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  48. I like the connection of this pattern with Sierpinski's triangle. I was expecting it to be a direct Sierpinski triangle, not a "higher order" one with many more smaller copies of itself in the central triangle though. I also saw the symmetries of rotating the triangle and running the rules that way. I now wonder if it's possible to "run the rules in reverse" and build up the triangle that way? It doesn't really look it's possible with this rule set, but is there one that can?
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  49. Great video! The concept of what shapes can be made from a number of small squares has interested me in terms of number theory and prime numbers. Obviously a number of small squares can form a rectangle if and only if the number is composite and conversely if a number of small squares is prime it can not be formed into a rectangle. If anyone knows of any material that explores that aspect of the square tile re-arrangement subject it would be greatly appreciated. Thanks again for the great content!!
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  50. Vielen Dank für das tolle Video!
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