Hearted Youtube comments on Mathologer (@Mathologer) channel.

  1. I'm from India and study in a particular syllabus called ICSE. Heron's formula is a compulsory part of the mathematics syllabus starting from Year 8. However, we only learn and use it in the √s(s-a)(s-b)(s-c) form.As for my opinion on whether it is useful, I think it is very handy to have learnt because you wont always have the height of the triangle given as data. Thanks for the amazing clarification on how the formula was derived.
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  2. Nathan's problem: Prove a sequence of "1"s for face-down cards terminates in a sequence of "0"s for face-up cards. Only valid moves are "11" becomes "00" (net of +2 face-up cards or -3 in binary) , "10" becomes "01" (net of +0 face-up cards or -1 in binary), and "1" becomes "0" (net of +1 face-up cards or -1 in binary). Each of the moves results in [0 to 2] face up cards or [-3 to -1] in binary.
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  3. When I learned calculus, I always seemed to screw up the algebra and not the calculus.
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  4. Amazing! As any of the Mathologer's videos. This is by far my favorite channel on YouTube. Thanks!!
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  5. I think the paradox partly comes from the fact that you can't compare surface area to volume at all. If some object you measured has the same area and volume, it's the consequence of your units and not the object itself.
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  6. That trick of finding a less restrictive form and finding that your proof is simpler there is a common one.
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  7. "Very nice song" is a link back to this video Prof. Hardy's life appears to be increasingly anticlimactic. Always overshadowed or outdone, it seems.
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  8.  @kenhaley4  Fixed the link :)
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  9.  @andlabs  Fixed the link :)
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  10. I'm a brazilian olympiad student, the time I traveled to where I was going to participate in Conesul (South America Olympiad) there was a training during 3 days before the test. One of the problems that my professors showed was this one, pretty fun problem, by the way. My solution at the time was, without loss of generality fix the point that's gonna be reached by the soldiers, and say it has an energy of 1. And then, the natural ideia that came in my mind was to say that any square that was K squares apart from the square we're going to has an enery of (phi)^{-K}. Like this, as well as your solution, the energy of the whole table is always, at least, preserved, and summing the energy of every square below the red line equals something less than 1 (which you can easily compute by some infinite power sum tricks). It's always great to watch your videos! thanks🇧🇷
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  11. 22:02
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  12. @19:04: to get the sequence of fractions, start with 1/1 = a/b. Then, given the current faction is a/b, the next fraction is (a+2b) / (a+b).
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  13. Another great video! Thank you. BTW that rotating hypercube at the end is a torus whose surface rotates around the poloidal axis while remaining fixed on the toroidal axis. An interesting video would show rotations about both axes simultaneously.
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  14. Whoa, getting name-checked in a Mathologer video! Achievement unlocked!
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  15. Yes! You can also prove that for any n different coin denominations, the number of ways to make change out of S bills, each bill with value the lcm of the coin denominations, is a polynomial in S.
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  16. "Our summation formulas are some sort of weird inverse of Pascals triangle" - Mathologer 2019
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  17. Third puzzle: :o 3D: :0 30-45-60: :O This was so cool, thanks!
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  18. MATH QUESTION A |\ | \ |. \ B |.___\. C ABC is right angled triangle, AB = 1728 BC = 1050 AC = ? (Write you answer in reply section) HAPPY NEW YEAR EVERYONE
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  19. Beautiful. And that is just one of the all-dimentional superfigures (I just made up the term) : hypercube. There is also simplex (triangle-based), and a strange weak superfigure, which is a hexagon in 2d, dodecahedron in 3d, another figure in 4d, and then it dies. But... a question: What about the doubles? the double of the cube is an octahedron. Does it have its own formulas, extending through all dimensions? What about icosahedron (the double of the dodecahedron)? Thanks.
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  20. "are there any more triangles that work" wouldn't building a width 10 out of width 10's work... you can treat the width 10 as a single unit of three then this pattern can be expanded forever...
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  21. I didn't rewatch it entirely, but I enjoyed the new part and I did play it entirely nevertheless; now I also commented, and I gave it a like, which I rarely do. Lets see if we can let THE ALGORITHM bite its own tail!
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  22. this blows my mind
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  23. Reminds me of something i looked into once: the random harmonic series. That is, the harmonic series with the sign of each term chosen by a coin flip. The resulting series converges almost surely, and it turns out it has some neat properties as a random variable.
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  24. Thank you so so much
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  25. 11:58 One small correction. The golden spiral is not made up of quarter-circles. It is the logarithmic spiral with growth factor φ. The succession of quarter-circles approximates the golden spiral. A Fibonacci spiral also approximates the golden spiral, with the approximation improving as the number of squares increases.
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  26. My problem with Mathologer videos: do I watch it now or do I save it until I cook up a gigantic traditional Asian meal to go with it?
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  27. hello mathologer. your content brings me such incredible joy and I am so grateful for the effort you put into making this beautiful mathematics accessible. although I had to replay the level 4 section once or twice to understand the recursive field logic (I am also rather drunk), I feel I have taken a relaxing tour and come out with a strong barebones understanding of the proof. at the very least, I leave this video with a deeper appreciation for our human struggle which unites us over time and place to evolve our logical tools. what an incredible triumph for wantzel, whom I have learned died only at 33 but will live eternally in legacy. (although he had more time than galois.) let us learn not only from his proof but also from his example, and practice moderation in excitatory drugs and late night mathematics!
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  28. to the window to the wall
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  29. I’m glad I’m not the only one hung up on that. I was half-expecting him to go, “Oh by the way … figure out what’s wrong with this picture.” He’s done it in other videos before, so it would be on brand!
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  30. Answer to the card question: Q of H?
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  31.  @Mathologer hi
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  32. Now we all know why atmospheric pressure is measured in TORR (a unit of pressure that is equal to 1/760 of one standard atmosphere. One torr is approximately 133.32 Pa)!
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  33. 28:13 my high school teacher showed this to us once, and then he proved it to explain how proofs by induction work!!
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  34. By bloopers, do you refer to the formatting inconsistency? For example, 二百五 is "two hundred five", so 205. Next to it is 九八七, being "nine eight seven", which is contexts like this would refer to 987. In these settings, you'd just list the numbers off one by one. You wouldn't give the full name. A bus numbered 64 would be read as 六四, which is "six four", rather than 六十四, which is "six ten four", so "sixty four". Basically, you wouldn't have things like 白 (hundred) in this sort of thing. Just the base characters listed like a phone number.
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  35. did you know that if you square the Fourier series of f(x)=x between [-T,T] and equate its infinite coefficients with the coefficients of the Fourier series of f(x)=x^2 in the same interval, one gets all the identities of even powers of pi at once?
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  36. Channel 6 Challenge: (Some space to prevent spoilers, you have been warned.) 1, 2, 4, 8, 16, 32, 64 Using binary, any given number can be uniquely made by some combination of those 7.
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  37. Long waited 💪
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  38. This lends itself to turtle graphics, via the The Total Turtle Trip Theorem, which states that the turtle will draw a closed figure with n sides when the sum of the angles turned is a multiple of 360. (From Turtle Geometry by by Andrea diSessa and Hal Abelson)
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  39. Με αρεσκει.
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  40. I would guess same diameter ;) Nice content, Nice video name, thank you for the chronological facts too.
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  41. Banger video as always!
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  42. There is something weirdly relaxing and also beautiful watching the animations and the number somehow forming! ❤
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  43. really liked this one!
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  44. I am Dutch and a huge fan of the Mathologer way of explaining mathematics. F.J.M. Barning is Fredericus Johannes Maria Barning, in daily life he was called Freek Barning. He died in 2012.
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  45. SOOOO AGREE!! This guy makes math MAKE SENSE!
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  46. Domotro!
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  47. Now I see why it is "one sentence proof". Because most part of the proof is in visuals, not in sentences :)
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  48.  @wolvenedge6214  Yeah, I realized as he went along that the user is choosing more terms in a certain direction to ENSURE arrival at predetermined sum. This still leaves my intuition feeling that if the chosen number is positive, then the sum MUST contain more positive numbers than negative ones...then again...even that can be shown to be untrue, cuz one could arbitrarily choose more (but very small) negatives, and fewer (but very large), to arrive at the same number. Finally, however, the systematic "rule" that Mr Polster used, isn't arbitrary! I still feel the infinite positive set is larger than the negative set! BAH!
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  49. Well done with the video. I had to watch it a few times to understand it all! I was OK to the halfway point then started to struggle, but stayed until the end. Thank goodness for the chapters. Keep making them.
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  50. Absolutely amazing! blown away! what a great presentation, Mathologer!! You made my day!
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