Hearted Youtube comments on Mathologer (@Mathologer) channel.

  1. 20:57 As a French, I was taught "ln" stands for "logarithme népérien" after John Napier, discoverer of logarithms (John Napier's name is often francizied as "Jean Neper").
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  2. math good yes very math number
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  3. The problem I see with the contested garment rule is that it promotes people claiming as much as possible, preferably all.
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  4. To honor Madhava of Sangamagrama, there's a (rotated) indian flag in the lower left corner at 11:40. Unintentional Christmas egg?
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  5. I'm from Kerala and I am feeling proud after seeing Malayalam.
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  6. 2nd puzzle is easy. (2*365)/365. And yes, I also noticed those patterns and extended them to 0. Tried to look for other ones with different exponents (after I learned of Fermat last theorem, I looked for non-positive and non-integer exponents), but to no avail. I always liked that first pattern doesn't have a "hole" - so it uses all numbers. I always wondered if the unused numbers in 2nd pattern can be used for something. I guess I will sit down with my pen and paper later this evening to check if there isn't some interesting there. Even if not as beautiful.
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  7. How do you prove ramanujan’s continued fraction for phi? Or formula for pi?
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  8. I did not expect to ever see the trollface in a mathologer video 😂
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  9. 15:35 very nice way to teach binomial coefficient
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  10. It always kills me that Tesla died alone and penniless.
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  11.  @jannikheidemann3805  I don't know. I'm from Germany. I grew up in the 90s an 00s.
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  12. My school in Britain taught Latin. I think Latin was an essential requirement if you wanted to be accepted as a student in Oxford and Cambridge Universities. A little indicator of a well educated candidate. Not any more of course!
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  13. 8:10 that's a big ππ formula indeed
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  14. Hallo Burkard, Ich schreibe Dir einfach mal auf Deutsch, weil mir das ein bisschen einfacher fällt. Ich möchte Dir einfach mal Danke sagen! Dein Video zur quadratischen Reziprozität hat mich zum ersten Mal mit der modularen Arithmetik in Kontakt gebracht und, was soll ich sagen, jetzt bin ich im JugendForscht-Wettbewerb (in der Altersparte "Schüler Experimentieren", weil ich noch etwas jünger bin...) Landessieger in Berlin mit einem Projekt aus dem Fachbereich Mathematik, inspiriert durch Dich! Falls es Dich interessiert, die Preisverleihung ist auf dem Youtube-Kanal des innoCampus der TU Berlin zu finden. (Es ist ja alles digital gewesen; ich bin ab 40:24). Es ist wirklich schön und auch irgendwie beeindruckend, was für ein Projekt aus dieser Inspiration und diesem tollen Video entstanden ist. Ich weiß noch, als ich diesen ersten "Wow!"-Moment hatte und bis nach Mitternacht wach war, um die ersten Ansätze auszuarbeiten. Ich finde es überwältigend, was die Mathematik bisher alles Großartiges bereitgehalten hat, was ich dann entdecken durfte, und das alles nur Dank Dir! Ich bin mittlerweile sogar soweit, dass wieder einen Bogen zur quadratischen Reziprozität selbst bekommen habe! ;) Aber auch generell möchte ich Dir einfach mal danken für Deine tollen Videos, die mir durch diese schöne Mathematik immer wieder den Tag versüßen, wenn nicht sogar der Höhepunkt sind! Sollte Dich vielleicht interessieren, was ich so gemacht habe, kannst Du mich gerne kontaktieren! Viele Grüße und noch einen wunderschönen Tag, Tim
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  15. Well, you’ve set me down a rabbit hole again for at least the next week. Amazing video as always!
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  16. Thanks for the mention! I love when I stumble across a comment like this, especially on a channel as great as Mathologer :)
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  17. 46:28 okay, now that is the sneakiest conjugation I think I've ever seen
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  18. The thing about Euler's solution to the Basel problem is that the maths in it isn't actually very hard to follow, it's sixth-form-level stuff really. But the reason the Basel problem stumped the likes of Fermat and Bernoulli was because the solution requires thinking outside the box, and skating on thin ice with regards to mathematical rigour. Euler took a few steps that more experienced mathematicians might have disregarded as nonsense - but he got the right answer, didn't he? It was Euler's creativity that was what really unlocked the problem.
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  19. No. The counterexample is easy, remove a2, a3, b1, c1. a1 is isolated and therefore no tiling is possible
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  20. Video uploaded 1 minute ago and already had 5 likes. I am really impressed by the amazing mind power of mathologer's viewers where they fast forwarded a 40 minute video to watch in 1 minute and still understood it well to like the video at the end. Or may be they used some kind of algorithm i am mot sure. Great job guys!
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  21. 31:00 I guess the Queen of Hearts is the missing card.
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  22. Had an incredibly rough week, this was precisely the pick me up I needed!
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  23. Hero's formula for the area of a triangle is one of those things introduced as a curiosity in a math textbook way back in middle school that I never really got a handle on. To a sixth grader, that is an impressively complex formula for an ancient to have discovered, and no proof was forthcoming. Through high school I saw it a couple more times, always in passing, a sort of neat oddity that seems compact but rarely gets used in practice. It was really neat to see an intuitive proof and motivation after all these years. That said, it doesn't exactly seem useful. Even if you somehow do know the lengths of a triangle but not its angles, this formula is still not the fastest way to find the area. Typically, if you're doing this by hand, you will either have a table of square roots (for Hero's method) or of logs and logs of sines (for the law of sines method). That method is still faster, because you skip all the multiplication steps. If you want to compute the area of the triangle with a computer, you can use Newton's method to get the square root, and I assume Heron's formula really is faster. But the thing is, you basically never know all the side lengths of a triangle (and nothing else) before trying to find its area. Rather, you probably have coordinates, in which case the shoelace formula is by far the fastest. So like, what is this formula actually good for? Is it just a novelty like the quartic formula? If it's never used, then no, I don't think it should be taught as part of a standard curriculum. The brief mentions in books for interested students are probably enough. There is so much I want to add to the math curriculum, and the curriculum is already packed as it is. It's hard to justify cramming in more random formulas to teach, prove, and memorize. (BTW, although the phrase "Heron's formula" is seen pretty often in mathematical texts, in pretty much all other contexts in English, "Hero" is far more common than "Heron." Similarly, we say "Plato" rather than "Platon." The practice of Latinizing ancient Greek names is pretty standard in English. In classical Latin, the nominative singular would be "HERO," and the genitive singular would be "HERONIS." Since the Latin stem is still Heron-, the English adjective would be "Heronic" rather than "Heroic." Again, that's like the adjective "Platonic" rather than "Platoic. Other examples include "Pluto/Plutonic" and "Apollo/Apollonic." Admittedly, there are some exceptions, like the word "gnomon.")
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  24. It's 12:05 AM here, what a Christmas gift mathologer thanks! 😍
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  25. fascinating, I could watch you for days!
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  26. Can we get a round of applause for the most inefficient way to calculate factorial?
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  27. What a delight to watch your video's! Being a math teacher myself, I cannot help but notice the similarities in how we teach. Especially the animated (sometimes hand wavy ;) ) proofs are sublime. Most educational math videos on YouTube sure lack proofs and just summarize/explain statements. Hats off to you dear Sir! Hopefully you'll keep on educating us all!
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  28. For some reason, I'm gonna remember this video as the Pigeon Pizza Pi Hole Principle.
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  29. The connection to physics: If you have a physical wave with frequency 10Hz, and another with frequency 4Hz, you get an interference pattern. Map this with a fourier transform onto a circle and you see a recurrence. Now if you change one of these waves to be non-constant frequency…. Which is not mysticism, but understanding the effects of repeated physical interactions.
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  30. 28:34 Wait a moment! Take a closer look at the second row... where's the 5? xD
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  31. If you find the “infinite tail of zeroes” hard to swallow, it might help to realize that the only thing that controls whether a particular fraction has an infinite tail of zeroes or an infinite tail of something else is your choice of numeric base (which is not a fundamental property of numbers); for example 1/3 is 0.333... in decimal, but it’s 0.1 in ternary. If you’re still unwilling to accept tails of infinitely many zeroes as equivalent, then take this: 3/4 = 0.75 = 0.75000... but also exactly = 0.749999999... a sequence of infinitely many 9’s.
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  32. This is really interesting! Thank you 💕 You are my favorite math youtuber! <3
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  33.  @maypiatt3766  and this channel is also inspiring mathematic thinking and curiosity in many 13 year olds (like me)
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  34. Thanks for this video. It was a wonderful presentation on a usually very stuffy and difficult subject. I honestly cannot say that I (PhD applied maths) was able to follow everything while I was watching the video, but it showed me one very important thing: that I skipped numebr theory, Galois theory, extension fields and so on for all the wrong reasons when I was studying maths at uni. If they had explained to me then that it would give a lot of insight into the boundaries of what is possible with Euclid's geometry I would have been all over it.
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  35. 42:05 My Memorable part: As Always It Goes to Euler. The Gamma : )
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  36. I don't remember doing anything in primary school involving indices including ^2 for 'squared', we did areas of shapes by counting squares on squared paper, nothing about algebra either. It was all new in secondary school. The first year there (ages 11-12) was basically doing catch up for what we should have/could have all learnt in primary school, but without a 'national curriculum', each junior school had probably taught different things and missed some things out. I think things have probably improved since then with maths teaching, but some (10-12 year olds) still seem to struggle with the basics - because of not learning times tables, or because new maths concepts are not introduced in a simple way, avoiding using complicated language.
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  37. Makes me wonder just how much of mathematics can be reduced to stuff that's easier to understand.
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  38. and here i always wondered how mathologer decides on topics - another mystery solved
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  39. Mathologer I think there's a mistake at 16:49 - the x at the top is missing a power of 0
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  40. Wow astounding how they could have done all this so long ago!
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  41. I learnt Heron's method of finding area of any triangle by myself from a mathematical formulas Book , when I was in 8th class in the year 1988. Even today I find it useful in my field works 👍
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  42. my high school had a copy of that same book, Thompson's "Calculus Made Easy". i remember using it to teach myself calculus before i ever took a class because i wanted to help my girlfriend at the time with her homework lol
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  43.  @cliveso  Yes, if each creditor divides their loans proportionally to the loan size, then you give disproportional advantage to the largest creditor. But if assume everyone is equally determined and thus able to divide their loans as much as everyone else, then you get a stalemate and no one gains any advantage
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  44. A motivational video for discovering mathematics.
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  45. The problem with the sphere seems to be a matter of curvature. The angles of triangles with flat curvature will always add up to 180 degrees no matter how small they become, and so there will always be extra area at the points.
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  46. The way I went: there are 33*33=1089 tiles on the board. The sum of all tiles 1 to 1089 is the 1089th triangular number: 1089*1090/2=593,505. Divide that by the 33 tiles in any row, and you get 17,985.
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  47. Such another great piece of art you were able to produce! I like the pure mathematics combined with the archeology. Isn’t is amazing that we just slowly discover how far advanced medical scions was advanced? I am so glad that we are now more open minded and allow to combine the facts of the past. Past scientist would have been happy and proud of us seeing the collaboration and joy.
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  48. It’s interesting to consider this prospective of the logarithmic product rule in the context of primes, the prime number theorem, harmonic series, and Reimann Zeta function.
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  49. Pick's Theorem! Very nice idea. You don't actually need the full Pick's theorem, only the fact that the area of any polygon with vertices on the grid points must have rational area, which is pretty easy to show.
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  50. It’s been years since I’ve seen these proofs but I was taught the second one first. I love the visual explanations. Great video.
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