Hearted Youtube comments on Mathologer (@Mathologer) channel.

  1. How on earth could you resist to check what happens with the sequence of primes??? Thanks for the video.
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  2. This the the only strand-type math problem
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  3. I have a bachelor’s degree in mathematics. I was able to follow everything except for the formula at 40:45. Im sure that requires more thought/explanation but overall, great video.
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  4. I wonder if Neil Sloane might be interested in including this Moessner-Transform and reverse transform into his database of integer sequences.
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  5. The visualization for finding the base (14:30) to (16:30) is marvelous :D
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  6. I was watching one of your videos about infinite fractions and... WOW, NEW VIDEO, THAAAANKS
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  7. I feel like a similar version of this problem is in NCERT Ex. 5.4 (Optional) Class X Mathematics. Who else have tried that problem using AP?
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  8. When I saw the 1+1/2 case for figuring out the base (and mentally extrapolated the rest of the proof), I was shocked- such beauty!
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  9. For the m x n board with m and n being odd numbers: Since m and n are odd, the denominators (m + 1, n + 1) in the fractions inside cos will always be even. And, since we round up in the expression above the PIs, j and k will in one factor both be exactly half of m + 1 and n + 1 respectively. When this happens we get cos(Pi/2) for both terms. Squaring the cos of course changes nothing. And when the product has one zero factor the entire thing will equal zero. Much fun this one!
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  10. You make complicated-looking maths problems sound so easy! Please keep up the great work!
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  11. I'm pretty sure it is the case that debts are consolidated before shares are calculated. The only way to have multiple claims is to have multiple legal entities asking for compensation and the courts not noticing that they are same creditor. That means that splitting up loans into smaller claims is not a useful strategy.
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  12. It’s always interesting seeing how close genuine mathematics, particularly number theory, gets to numerology sometimes - the choice of base ten is essentially completely arbitrary. On a barely related topic, I would love to see a video which covers some of the bignum arithmetic algorithms, like karatsuba, toom-cook, and possibly even FFT based multiplication. We rely on these algorithms thousands of times per day for RSA in TLS, so I feel they deserve some love.
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  13. Pretty sure that wheels made of logs is a very old invention ... this one just added special Powers.
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  14. There is a special place in heaven for people like you who make math accessible and fun, who put the intermediate logical steps in their demonstrations, thank you.
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  15. Removing two black and two green cannot always work. By counterexample: you can isolate a corner square. But sometimes you *can*: example: just remove the squares occupied by any two dominoes of a domino-filled chessboard.
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  16. Like others, I'm an old engineer who used a slide rule during my exams at university: cheap calculators hadn't been invented yet. (I still have my slide rules.) I also noted that log graph paper has the scales exactly the same as that of a slide rule. So when I was travelling in the UK after graduation (and before calculators and phones), I cut out two of the axes on the graph paper and taped them to cardboard at the proper point so that I was permanently calculating the conversion between Canadian dollars and pounds Sterling. While shopping, I could easily convert an item's cost to familiar currrency.
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  17. Mr. Mathologer. Thank you for your good work. I understand every single thought, every single word in every single second in this video and it is an extreme pleasure to follow the steps of these old math geniuses. The perfectness and beauty of math amazes me for years now. And it never stops. In math we see ... god.
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  18. A teacher showed me this back in high school, and I thought it was really pretty. I had wanted to include it in my combinatorics series, but I had to cut it for time. Great to see it covered in Mathologer fashion.
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  19. 13:27 In 1,023 moves, moving the smallest disc every other move means we're moving it 512 times, which is 2 (mod 3). So we need to move it counter-clockwise (A -> C -> B -> A) to make sure it ends at B. In general, 2^(n-1) is 1 (mod 3) if n is odd and 2 (mod 3) if n is even, so we should move the smallest disc clockwise if n is odd and counter-clockwise if n is even.
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  20. I'm a finn born in 1960. When I got my groung schooling it was given that I need to learn germany as most of the books in the universities in Finland were written in germany. The time (1981) when I entered uni in Helsinki, Finland to study mathematics, all the books were written either in finnish or english.
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  21. ​ @Mathologer  that's the sad state of affairs today sadly 😔
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  22. I have always thought about the coin rotation “paradox” in a rather simple manner. The distance travelled by a coin with radius r around the outside of another circle with radius R is simply 2*pi*(R + r), or 2*pi*(R – r) if it travels on the inside. Given the constraint of no-slip and the correct ratios, the result is hardly surprising.
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  23. I'm a High Schooler, didn't understand some parts😁. But I enjoyed the video so much🥰🥰 . Whenever I watch these Mathologar videos everytime I learn a new thing beyond High School syllabus. I just love this channel, he teaches in a very creative,fun and funny way.
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  24. (OH)4: A Christmas joke for innumerate dyslexics
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  25. Another masterpiece as always. I am a math nut, have been my whole life. When I go for a walk I think about numbers and sequences and formulas and physics. I spent my career as an engineer but now that I am at retirement I spend large amounts of time on 2 of my loves - math and physics. This is am absolutely fantastic channel. Thank you!
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  26. An Italian Math and CS Senior Lecturer here. Just want to share that, as it happened to the Mathologer, when my professor did the Riemann rearrangements theorem in Real Analysis I, as a freshman, was totally upset and amazed by this counterintuitive result. Congrats to The @Mathologer whose videos always make us see the things we know under new and interesting perspectives.
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  27. Me: takes out ring, proposes GF: says yes, crying Me: starts talking about the number of vertices on the diamond of the ring GF: takes off ring
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  28. I'm amazed that the paraboloid & the parabola were even known and studied that long ago. How did they define it without coordinate geometry?
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  29. Is asking people to spam "I made it to the very end" a way to drive eNgAgEmEnT?
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  30. I just realized: for the hexagon, if you turned it into a 3D broken cube, then looked at it from any of the open faces (assuming you're looking directly at the face from a single point), you would see a complete square of one color. This would be the same from all three open sides, and there would be no hidden faces. Thus, the sides being equal, there will always be an equal number of each color domino
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  31. 13:00 My guess: a^2 = a×a, so I think the output sequence will be a^a.
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  32. My favorite fact about the Dürer magic square: it was completed in the year 1514, and in the middle of the bottom row you can see it says 15 14. The only similar example I know of is the Basel problem, posed in 1644 whose solution is pi^2/6 = 1.644... However, sources differ on whether it was first posed in 1644 or 1650.
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  33. I cant believe after all these years of calculus ive finally seen an intuitive argument for how lnx appears when integrating 1/x 😮
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  34. I was wondering what could possibly be interesting about the number of ways to tile the glasses. I couldn't have guessed it would be the number of the beast! I also didn't realise that the number of the beast could be written in a neat little expression involving only the first 4 primes: 666 = 3^2(5^2+7^2)
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  35. Mathematics is like an intellectual equivalent of Willy Wonka's Everlasting Gobstopper -- it is harder than anything else on Earth, it tastes wonderful and no matter how long you work at consuming it, it never diminishes.
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  36. 42:50 That time when you see Notch in the Paypals section
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  37. For the grid problem, sum up every the possible 2*2 suqare exactly once. Notice that the total amount of times red, green, yellow, purple appeared MUST BE EQUAL. The corner squares are counted once, the edge suqares are counted twice (it is calculated in 2 of the 2*2 suqare), and the squares in the middle are calculated 4 times(it is in 4 of the 2*2 squares). Since the total amount of 2*2 squares is ODD, every color must appear an ODD number of times. Ans since only the corner squares are counted an ODD number of times, each color MUST appear in the corner square. QED. By the same argument, we can show that every color appears on the corner of the 4n*4n*4n cube, if it is colored with 8 colors such that every 2*2*2 cube consist of 8 distinct colors. We can generalize this further to m dimentional cube with 4n as its sides.
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  38. Not as had as "what comes next in the following sequence: 1, 3, ? " Answer "TREE(3)", not acceptable, must give an exact integer value.
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  39. Very much so :(
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  40. It makes me happy to see someone as famous / well-known as you acknowledge a mistake, own it, and correct it. As a fellow mathematician / professor, I genuinely appreciate the humility you have shown!
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  41. Congratulations on 100 videos! Your channel is awesome ❤
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  42. When the rubber band snaps you get the so-called "broken numbers", which were studied in 1763 by mathematicians working in a causally-disconnected region of spacetime, so unfortunately we will never find out what they discovered.
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  43. 4:54 This actually isn't quite the origin of the name. From Wikipedia: Dirichlet published his works in both French and German, using either the German Schubfach or the French tiroir. The strict original meaning of these terms corresponds to the English drawer, that is, an open-topped box that can be slid in and out of the cabinet that contains it. (Dirichlet wrote about distributing pearls among drawers.) These terms were morphed to the word pigeonhole in the sense of a small open space in a desk, cabinet, or wall for keeping letters or papers, metaphorically rooted in structures that house pigeons. Because furniture with pigeonholes is commonly used for storing or sorting things into many categories (such as letters in a post office or room keys in a hotel), the translation pigeonhole may be a better rendering of Dirichlet's original drawer metaphor. That understanding of the term pigeonhole, referring to some furniture features, is fading—especially among those who do not speak English natively but as a lingua franca in the scientific world—in favour of the more pictorial interpretation, literally involving pigeons and holes. The suggestive (though not misleading) interpretation of "pigeonhole" as "dovecote" has lately found its way back to a German back-translation of the "pigeonhole principle" as the "Taubenschlagprinzip".
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  44. 24:30 It's "obvious" because 1/x is concave, meaning between any two points the graph is below the secant line connecting those two points. Dividing the 1x1 square into rectangles in the obvious way, the blue areas include more than half of each rectangle and hence more than half of the 1x1 square.
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  45. As you were finding the tiny areas and adding them up, I couldn't help thinking that essentially the Jacobian is involved. If you don't get the Jacobian right, your area won't be right. That is, the Jacobian is what tells you how to get areas right. And it is also related to your little spikeys.
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  46. Very subtle post dubbing in the last chapter ;)
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  47. Mathologer walks into a party "Hey wanna see a card trick?"
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  48. 2^2+ i^2=3
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  49. 👍
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  50. Almost number of the beast. In Dutch we called the slide rule a “gokstok” (gamble stick). In English this device could be the “wheel of fortune”.
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