Hearted Youtube comments on Mathologer (@Mathologer) channel.

  1. The entire video I was wondering what the 2 in the (x+2) formula was really referring to. Sooo satisfying to see the recurrence equation at 25:00, makes so much sense!
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  2. Undergraduate student in physics here, more into theory side of it so I know some difficult maths Finished the video and went: yep i understand everything and yet remembered nothing xD went back and looked through the formulas again, beautiful stuff oddly it doesn't feel like even 20 minutes had passed for me... ah yes, i was watching at x2 speed with a lot of pausing and backtracking :l the math used in this video is considered 'basics' for me, yet the application is mind blowing nonetheless soooo... "yes please make more videos i would pay for them even" "I am thinking of finally putting up a Patreon page. What sorts of things would you like to see there?" ... well, yes. also maths and perhaps some math story you find fascinating (as for 'is the video too hard for the general audience'... well... i am not an accurate reference) Thanks for the lesson!
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  3. My vote definetely goes to Kempner's proof, it is extremely elegant, since the concepts used are individualy simple, such as the calculation of numbers without nine or geometric series, but when cleverly combined they form this amazing result. Besides that, great video as always. Edit: typo
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  4. As a mid-level PowerPoint wizard, just be glad you didn’t have to use google slides. Those animations looked difficult enough as is.
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  5. Numberphile also a Ptolemy video 4 years ago, featuring Zvezdelina Stankova. Also enthusiastic, but with very different twists.
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  6. A short video on change
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  7. I mean I cheated or crammed my way through high school I was too bored to try, so this is the first time I’m seeing these design elements explained from a mathematical standpoint which helps me understand them deeper: It’s amazing how intertwined art, beauty, mathematics, numbers, algorithms, patterns etc. Truly all connected. I am all that is, because all that is - is within me. 🙏🏻
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  8. @ Everyone would divide their loans into the smallest chunks possible, until the admin costs outweigh the gains. The admin costs will determine how small the chunks will be.
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  9.  @Mathologer  yes, I remember to have watched that one a long time ago. I just rewatched it. (It's now 2:41 am, I should be sleeping already). I am pretty sure I understood everything you did there, but to be sure I'll rewatch it a second time in a few days. But I'm really waiting for the "completely insane" (yes that was your real promise) Level 7 of this video. Galois theory. I love completely insane video's. It will, I already am sure about that now, probably be the most interesting and exciting masterpiece you've ever made as mathologer. All the best, A.
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  10. animation autopilot is getting smoother day by day (I can see the damn hard work) Merry Christmas mathologer and wishes for another year of masterclasses.
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  11. It's those diagrams and cool connections that make me love number theory. Please do more number theory videos.
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  12. Marble: Most memorable Idea: No integers among the partial sums. Your excitement is always a great feature not your presentations. And why you're my favorite Mathematics YouTuber!
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  13. I reckon the Iron Man title is more enticing than the +/- title. I had not cheched the video before, seemed such a dense, intimidating subject. Now it's like discovering an easter egg of the MCU, seems worth enduring the hard maths somehow.
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  14. Such a scheme can be used against any creditor, which is why we have a regulated bankruptcy process: you can seek and get future protection from your creditors, but you must reveal under oath all your assets and claims against others in return. The bankcruptcy court will divide most of your assets among your creditors but grant you bankcruptcy protection from your creditors for the future. However, if you hide that scheme you and your friend have agreed upon, you commit bankruptcy fraud, which is a felony.
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  15. If we somehow were able to get back the burnt books of Nalanda University, then I am pretty sure that more than 90% of today's "modern" discoveries in maths and science would be found in them.
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  16. Wonderful video as always. The more videos I watch the more I'm convinced that Euler must've been a time-travelling Mathologer viewer who really wanted to look smart by appearing in every video
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  17. reads how to make googol dollars Nobody: Bill Gates and Jeff Bezos:That’s not a dare, that’s Tuesday.
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  18. This channel is great like its viewers. We always get excited when notification popped out.
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  19. just wanna compliment the pacing of this video. first time i didnt have to pause/rewind to absorb, except when you prompted me to for the last chapter, which was when i was planning to take a break anyway lol
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  20. When I heard geometry and turtles, my first thought was Logo.
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  21. With a little bit of trigonometry on the heptagon, the set of equations for r and s can be used to show that cos(π/7) is the root of a cubic polynomial (8x³-4x²-4x+1=0). This immediately shows why the heptagon cannot be constructed (cube roots are not constructible). It's the same reason that one cannot construct a cube of volume 2. Using "origami math" (look it up, it's cool) one can construct roots of quartic polynomials. Geretschläger (1997) used this to construct a heptagon starting from just a quadratic sheet of paper (no straightedge or ruler required), but where you can make paper folds as in origami. The proof is given in the form of an origami folding instruction.
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  22. For anyone working on the problem at about 16:20 with derivatives, do yourself a favor and use (1-x)^(-1) instead of the fraction. Power rule & Chain rule is sooooo much easier than Quotient rule when it comes to taking more and more derivatives in this case.
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  23. So essentially if we were to rank lacings on strength and length 1 being the best and infinite being the worst we're looking for the lowest sum of the two factors to have the optimal lacing. The natural choice here would be the crisscross lacing. The crisscross lacing at best has rank 1 in both situations for a sum score of 2 and at worst it falls behind in strength on the zigzag lacing for a sum score of 3. The zigzag lacing at best will be 1st on strength and 2nd in length for a sum score of 3 which is merely equal to the crisscross in the same case. The case where they do equal at a sum score of 3, it would be a competition of preference where some situations might demand short laces by lack of material but some may prefer a higher tensile strength because they want to climb a mountain today.
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  24. It is nice to see this geometric approach to the topic. The result is not new to me, but the path 😊
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  25. You miss so much to talk about this more!! Do part 2 !!!!
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  26. The third edition of Proofs from THE BOOK also contains the proof, with all the details filled in.
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  27. I recently watched an interesting video featuring Roger Penrose in which he expressed the view, which I share, that mathematics is discovered, not invented. When I see patterns like this it further strengthens my view that maths fits together too beautifully and with too many hidden but elegant patterns to be invented. This was very interesting and no, I hadn't heard of Moessner. Thank you for another informative and well-explained video. The internet isn't just stupid cat videos.
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  28. I think the fact Gabriel's trumpet is infinitely long, makes it feel paradoxical. Because in my opinion, something like the Koch Snowflake extended in a 3rd dimension, to make a prism of finite volume and infinite surface area, intuitively feels less paradoxical. You can easily contain it within a cylinder. Yet, you can take it apart into infinite triangular prisms. Then you can stack those atop eachother to get a roughly trumpet-like object; which has the same finite volume, and has infinite surface area.
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  29. Wonderful! Spectaculary clear and teacherly. Richard Hamming's book "Numerical Methods for Scientists and Engineers" (a staple in engineering education 50 years ago) discusses "Difference Calculus" and "Summation Calculus" and describes "Summation by Parts" (!). For those of us who wrestle with numerical problems, all this material provides powerful tools and the basis for software algorithms that do the heavy lifting in science and engineering.
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  30. Everyone: maths is boring :( Mathsloger : let me take care of it. ;) Btw your videos are very interesting and full of knowledge...... Love from india 🇮🇳❤❤
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  31. I know "Numberphile" might be a complicated word around these parts.. but i will never forget watching that interview Brady did with him [Conway] when he's looking out the window and says "i wish i knew whyyy..." .. in reference to the strange universe-implying numbers in group theory - why the monster and no more?.. why any of the sporadjcs?.. especially when symmetry seems to play such a big role in fundamental physics
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  32. The challenge at 15:33, solved in a different way: The number of rotations of the smaller coin per each time it rolls around the bigger coin is equal to the ratio between the smaller coin's radius, and the distance between its center and the center of the larger coin. In the case of equal-sized coins, that ratio is 2, which explains why the outer coin rotates twice. For a smaller coin with diameter 2/3 of that of the bigger coin, its center is at a radius of 1/3+1/2=5/6, while its own radius is 1/3. (5/6)/(1/3)=5/2, so it should make two and a half rotations around its center for each time it rolls around the bigger coin.
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  33. You are very special. Thank you.
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  34. This is how far I could get equilibrating the cards from ace to king of diamonds: imgur(dot)com/gallery/6wJ657Q (I didn't put the link normally because youtube moved to spam)
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  35. ​ @josepeito Because their chief weapon is surprise 😆
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  36. Professor Polster, The Mathologer is THE best thing that happens to me in all of the media including Internet, blogs, youtube, social media, podcasts, TV, radio, movies, lectures, courses, and print. I can not describe how much pleasure I derive from watching Mathologer. At times, it's like a detective solving a crime (the crime being the difficult math problem at hand). Thank YOU, MARTY ROSS and OTHER GOOD PEOPLE who make Mathologer, such a good unusual program, possible. May you continue to produce your programs for at least another 50 years. Behnam Ashjari, PhD EE
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  37. Merry Cristmaths!
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  38. I remember coming across this formula at the corner of one page in my textbook in high school, and we just glossed over it.
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  39. 5^3 + 6^3 = 341, which is short of 7^3 by just two. I love that because you'd already mentioned trying to wrap a cube in square slices, I immediately imagined such a wrapping where two opposite corners were missing (though without checking I'm not sure that could really be done without further slicing the slices).
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  40. I live ~250km away from the birthplace of Saṅgamagrāma madhavan.
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  41. 13:00 Spoilers below! Using a=1, b=c=d=...=2, the highlighted sequence is 1, 2+2, 3+2+4, 4+2+4+6, ... In each term of the sequence, we can split up the first term of the sum into k 1s and spread them out over the rest of the terms of the sum, giving 1, 1+(1+2), 1+(1+2)+(1+4), 1+(1+2)+(1+4)+(1+6), ... Each term of the sequence is the sum of the first k odd numbers, which are the squares. That means that the sequence generated by the squares is 1, 2*1^2, 3*2^2*1^2, 4*3^2*2^2*1^2, ... In general, the kth term is k(k-1)!^2=k!(k-1)!
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  42. Congratulations on hitting 100 videos! That’s quite a milestone! Love your content, Mathologer!
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  43. Okay..Half way through the video..They do teach this to us..In highschool..But not in calculus..But in Sequences and Series under the name : Method of difference..Our teacher said.."When u find no other way(like the classic Vn method as they call it here) to find the General term of a sequence..Use this method to find it"
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  44. The hot topic in the last month has been AI. I have neutral feelings on the topic as it is just another tool and one that can be unplugged. The reason I bring this up is because the Indian Mathematician had to express mathematics with what was available to him, which was verse and not the concise mathematical language we have today, to borrow the term used in this video. At any rate, back onto my comment, Humans speak and think in verse, and maths is purely a symbolic form of logic to express patterns. AI works by using filters and approximations in much the same way as these approximations work and learns over time in much the same way. It is the next leap as it is even more efficient and concise than symbolism and mechanizes pattern recognition without the middle man of symbolism. The reason why it is frightening is because it does not give us symbolism to understand how it arrives at the answer. With each AI solution to a problem, cracking open that black box and seeing what steps the AI took to arrive at the answer might reveal a new level of mathematics or give insights for mathematicians to chew on.
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  45. You know what is really magical? You have made your instruction and animation line up, to almost create a gamified experience. This was wonderfully engaging and explantory, well done! Mathematical Tetris :)
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  46. 6:20 No, as you can isolate a corner, which clearly not be tiled over
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  47. I came back after long time ! what a beautiful voice 😗🙃
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  48. I studied electrical engineering and at University we learned something called symmetrical components theorem, of wich we use the specific simpler case for triangles. In reality we're not taught it as a triangle, but rather, as the three components of our three phase electrical grid (be it current or voltage). You see, in the electrical grid, the 3-phase system is not always symmetrical (with 3 phasors of the same length and 120° apart) because of asymmetrical loads and asymmetrical faults and such. So it would be very complicated to model and visualize it as a 3 phase system because of the symmetries. So instead, we model it as a sum of 3 symmetrical systems (analogous to those 5 symmetrical base pentagons). And seeing them as triangles would be like one equilateral triangle, one "mirrored" equilateral triangle and one "triangle" with all 3 vertices in the same location. It's sad the in my university we didn't go into much depth with this theorem, we just saw a glimpse of it and were immediately learning the application. But it's really nice to now see a video about it explaining everything in detail in an easy to comprehend format.
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  49. Hey I found 2019 in your π-shirt after the 244th digit after the decimal #yay
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  50. Professor, I am looking forward to you aiming at presenting the Galois theory the Mathologer way in the future. I have always considered the inability to solve quintics by radicals mysterious, hopefully your video will shed some light on the concept to non-mathematicians like me. Thank you very much for all the stuff you create, it is unimaginable to comprehend the amount of thought, time and effort to get such things done, with the above video being an excellent example.
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