Hearted Youtube comments on Mathologer (@Mathologer) channel.

  1. most memorable: ln(n+1) + γ and everything with missing numbers series ^^ !
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  2. My favorite part was when you revealed that the sum of the 100 zeroes series is greater than the sum of the no 9 series. Absolutely mind-blowing. In truth, my favorite part was the entire video you just made me pick :) Thank you!!!
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  3. yes i know how to do that puzzle. no there's no way in hell i'd get through the whole thing without screwing up at some point
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  4. Slightly disappointed that the Pell numbers (by name) and the silver ratio went unmentioned. It makes the continued fraction even simpler since, as a metallic mean, its expansion is just an integer repeating (i.e., the golden ratio's is 1 repeating, the silver ratio's is 2 repeating, bronze 3, and so on).
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  5. 14:53 Fun fact: The entrance to the Museum of Math in New York City is a glass cube, with this hexagon drawn.
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  6. No wonder Knuth mentions Concrete Mathematics every so often in TAOCP.
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  7. 7:14 Well, that's great and all but you won't be able to explain the OTHER gray number so easily. 7:46 Oh. Well, I'll see myself out.
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  8. Anyone else used these slide rules for "O" level maths ? Shows my age,eek!
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  9. One of my favorite channels on Youtube. Congratulations to Burkard and his team. Ausgezeichnete Arbeit! I always look forward to your new videos.
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  10. Somehow I guessed the rule. What do I get?
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  11. For those wondering what's wrong with the numbers - they are using decimal notation - they write 22 instead of the normal 2*10 + 2
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  12. Yea I think I could figure it out if I was in the Doctor's shoes, I figured it out when I was, Idk, early in my teens? And it's also mindlessly easy to execute if you get the first move right, everything else just falls into place. The Doctor is far smarter than me, and more experienced than I was or even am now
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  13. Being honest...I rarely make it to the end of a Mathologer video. In this case I've surprised myself by not only making it to the end, but in a seemingly too short amount of time. No video stretches like a Mathologer video.
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  14. By Pythagoras' theorem, the square of the radius of Conway's circle is the square of the radius of the incircle plus the sqare of half of the chord.
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  15.  @Hiltok  Here is a much trickier question: Which is larger, the area of Conway's circle, or the area of the shape of constant width?
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  16. For the Rubik’s cube order, I got 315 repetitions when I calculated the orders of all the edge and corner cycles (keeping track of piece orientations) and took the lcm. Recently I’ve been thinking about the connection between the pigeonhole principle and the Steinitz exchange lemma, since the pigeonhole principle could be seen as a consequence of the lemma with each of the pigeons and each of the boxes both being regarded as vectors over F_2, with the boxes forming a basis. While the latter perspective is overly complicated in this case, if you could find a different vector space that some problem could be interpreted in terms of, you might be able to use the exchange lemma in a similar way, but get better results than you would by using the pigeonhole principal directly. (The way in which the exchange lemma is used is that any collection of vectors with cardinality larger than the dimension of the space they are contained in must be linearly dependent)
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  17. 11:24 Looks like an origami Flower Tower. 😀
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  18. This has been a very helpful video. I'd been pondering how any island has an infinite coastline if measured to infinite precision yet has a finite land area, and had become stuck. This video came at a fortuitous time. Thanks for another great video!
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  19. Let A = Infinity 😂
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  20. awesome video! it's nice to see these types of problems be recognised
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  21. Mathologer it’s beautiful. Keep more of it coming!
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  22. I know about Moessner's miracle because I have the go-to Math bible - the Book of Numbers by Conway and Guy 😁
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  23. I would imagine it's true for all odd sized squares, but I noticed on the 5x5, that all pairs of squares that are 180 degrees opposite add to the same sum. I thus conjecture that for any 2k+1 square constructed in this way, taking k such pairs and summing them along with the center square will always sum to the magic total.
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  24. For the list which begins with 3^2+4^2=5^2. You had a short cut (formula) at the item before the equal sign. I have a short cut (formula) to jump from the last item of the previous line to the first item of the next line. 1st line ends with 5 2nd line begins with 10. Because 5 (last of previous line)/1(number of items on the right side)*2(number of items on the left side) 2nd line ends with 14 3rd line begins with 21. Because 14 (last of previous line)/2(number of items on the right side)*2(number of items on the left side).
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  25. I made it to the very end.. but it was NOT the same "I" that began.. i think..?
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  26. Although I'd be exaggerating if I said I understood this without reviewing some portions of the explanation, I believe the explanation was extremely well done! These videos are, for the most part, very satisfying mathematically. As some have already suggested perhaps we could one day find another human with the skill set of Ramanujan - but I'm not holding my breath!
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  27. This was fun. Thx. Peter PhD Theoretical Physics.
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  28. The diagonal construction of magic squares and the geo magic squares were both superbly presented... Really interesting!
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  29. plese make a video on master therom of RAMANUJAN
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  30. 16:43 when the doctor is sus
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  31. I was curious about what kind of wall would be generated from the prime number sequence.
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  32. plugging real numbers into the Fibonacci function and using complex numbers gives a nice exponential helix: the center follows exp(x) while the radius follows exp(-x) (or really, exponents of phi).
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  33. Amazing as always. Love it when you can start with a concept which is easy to formulate like ways of summing to an integer and end up needing e, pi, infinity and derivatives to express a general solution. Makes you appreciate how interconnected maths really are.
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  34. Hey can you please make a video on Telescoping Sums? Its a great method to solve sequences and series :)
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  35. this animation looks like a 4d shape of some kind i know it probably isn't one but it's still cool
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  36. K. Ramasubramanian is a professor at Indian Institute of Technology Mumbai. He is my favourite professor. The manuscript is his production.
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  37. Almost as excited to see the t-shirt as I am to hear the math!
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  38. 2:12 Consider the vertex of the triangle at the bottom-left. There are two lines going through it, both with red on one side and green+blue on the other side. Thus, the angle bisector of these two lines consists of all points that are equidistant from the red endpoints, and (separately) equidistant from the green+blue endpoints. But applying the same reasoning to the other vertices, this leads us to the intersection of all three angle bisectors of the triangle, namely the incenter. We have six equalities between the distances from the incenter to the endpoints, which combine to show that they are all the same! q.e.d.
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  39. 11:48 The box for 153^2 + 104^2 = 185^2 is 9 4 17 13. The upper two number can be calculated via: b = sqrt((z - x) / 2), a = sqrt((z + x) / 2) - b, where x^2+y^2=z^2. Then c = a+2b, d=a+b, in the form of: a b c d. The path there is: right right right left The algorithm to find the path to a given pythagorean triple in the tree: (x^2+y^2=z^2 , x,y,z ∈ N (0) Reduce triple to primitive triple by dividing by their greatest common divisor gcd(x, y, z) x = x / gcd(x, y, z) y = y / gcd(x, y, z) z = z / gcd(x, y, z)   (1) let a, b: b = sqrt((z - x) / 2), a = sqrt((z + x) / 2) - b   if a is even or either of them is not an integer or either of them is 0, repeat the calculation with y instead of x!   (2) Calculate the Category of a and b: C: N^2\{1,1} -> N   C(a,b) = 2 - floor(2 / ceil(2 * b / a)) for a != 1 or b != 1   if C(a, b) is undefined, jump to step (6)   (3) Save C(a, b) in memory   (4) Calculate a' and b' let c = C(a, b)   { a-2b for c = 0 a' = { 2b-a for c = 1 { a for c = 2   { b for c = 0 b' = { a-b for c = 1 { b-a for c = 2   (5) Repeat from (2) with a = a' and b = b' as long as a != b and a * b != 0   (6) Read the saved C(a, b) from (3) in reverse order 0 corresponds to going left, 1 corresponds to going straigt, 2 corresponds to going right!   DONE! Example code and Algorithm here: https://pastebin.com/T71NP8Z9 JS-Applet here: https://jsfiddle.net/ptu6f5cr/4/
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  40. 6:24 Sometimes you have to think inside the box
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  41. Herr Dr Polster: That was lovely. My chemistry teacher was like you, so I became a chemist. My maths teachers were terrible; but I like (love?) math anyway. I did have the calculus, some algebra which included Power series (which I never got), some differentials, partials, numerical methods, and so on. But I never got power Series at all until I just watched the Power Series Master Class. I got through all of it in two nights; I will have to watch it again and get out a pencil and paper to get more (Erdos: "if your fingers don't hurt, you're not working enough"). I got most of it, except the animation at the end, and I'm sure I must have missed something as I'm not that smart. But, thank you so much!
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  42. Finely an other mathologer video
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  43. Most excellent follow-up to the Fibonacci Flowers and the Most Irrational number videos. Loved the tree bit on the helicone! I appreciate the work and time you took to correct your small mistake. Your dedication to accuracy and truth is a worthy endeavor with manifest positive impact, and while it may be a given for you to be that way, I'll just point out that many many people don't operate like that, and in my eyes, this is a huge win for you because being open to correction and then correcting it looks better and is better than never making mistakes, because human. ❤
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  44. ??? The sum of the series is exactly equal to pi, 355/113 is not :)
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  45. dislikes are from casino managers
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  46. 15:00 Also; adding the 10th multiple-angled ears (in the case of the 10-gon; 5th multiple-angled ears, in the case of the pentagon), a.k.a. 360°-ears, a.k.a. line segments, to the point, will result, in another regular 10-gon (or pentagon, or n-gon). Obvious, I know. I just thought I’d point that out, lol. 😅
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  47. To be honest, "what comes next" questions don't even make sense. What relation is simple enough to be considered a "pattern"?
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  48. 21:15 shows the shrinking algorithm in real life. 🙂
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  49. The clip surely has olympiad level quality in playing on the audience's emotions with the visuals, ambience, and timing in delivery of lines.
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  50.  @Mathologer  MIND... ABSOLUTELY... BLOWN! Slide rules are complicated enough for me since I well and truly grew up in the age of digital calculators that can surf the internet, but to think that slide rules actually exist for complex numbers is beyond me! :learning:🤯
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