Hearted Youtube comments on Mathologer (@Mathologer) channel.

  1. 14:09 In this situation, the Torah is clear that it doesn't matter whose biological son the third son is, he would be legally counted as the son of the brother who died childless, regardless, so that his family line does not die out. That's the whole point of her marrying the nearest kinsman in the first place. The Talmud should not be contradicting the Torah on a matter like this, or on any matter for that matter.
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  2. I think one problem with the derivation is that we need to know if the infinite product converge before using it and that if we write sin(x) in function of its zeros, how we know that it doesnt have complex zeros that we need to add. Great video by the way.
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  3. I'm actually surprised and pleased with myself for being able to understand the solution from the clip alone, haha. Of course it is such a simple that anyone should be able to understand it, was is not for he using a binary number representation, and most people being unfamiliar with binary. If, for instance, he decided for no particular reason to use 0 and 9, everyone who isn't familiar with binary would immediately have an easier time understanding it. You can also describe the solution without using any numbers at all. You can just use the letters D and U, and show that the only two things that can happen to the sequence of letters is two Ds turn into Us, or a D swaps places with a U to its right. As a result you either end up with two Ds next to each other, or they are separated by some run of Us. In the latter case you can move the rightmost one until its all the way to the right, at which point the only remaining option is to move the leftmost D closer to the rightmost one until you're back to the former case, meaning you must turn both Ds into Us.
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  4. Hello sir , Namaste, I am big fan of your teaching.
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  5. This video was a joy to watch.
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  6. Imagine having a dad who can always help you with your math home work🤣
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  7. The # of steps is known. You always take those steps CLOCKWISE! The First person of the trick has a pair of cards to choose from. He determines the shortest distance between those two cards (circular measuring) and chooses to take away the card that is that many steps anti-clockwise of the other card. Example: player1 has to choose between Jack and 3. Shortest Distance = 5 (other distance =8). The 3 is the card taken away because then the player2 sees Jack + "code for 5 steps". So player2 knows he has to go 5 steps clockwise from the Jack and lands on the 3.
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  8. It will become...1M.....very very.....soon
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  9. You completely deserve it. A Mathologer merry chrismas to you
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  10. h³o³
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  11. Math is easy if you love it and understand why it happened :)
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  12. I'm not much into history or race when it comes to math. It's nice to notate who made what discoveries, but I care more about the how they figured it out than the who. Pride gets in the way of many things this way. ESPECIALLY in math as mathematics has nothing but facts to give us. No politics, no pride, no religious...just facts. Noting that the discovery was made earlier gives us factual view of history that says we weren't just mud and straw builders and DID have the knowledge to accomplish great feats of engineering. I enjoyed your video immensely.Thank you so very much.
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  13. I studied maths for six years after my high school degree and, still, I learned so much in this video! Thank you Mathologer for all the wanders you bring us. :)
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  14. My God that was mindblowing, this channel has me obsessed!!! Everytime I watch a Mathologder video, I can't wait to explain it to everyone I know (though they aren't math nerds like me :D)
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  15. First
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  16. Dear Professor, another shining explanation about a brilliant gem. Thanks a lot. Again: this is my favourite channel EVER!
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  17. Kudos! To think that such simple principles could go unnoticed for so long. Which is why I love this channel, come to think of it. Not only is the content absolutely amazing, I always feel like I've learned something new. (Almost as if taking a glimpse into the realm of "sacred geometry" or something!)
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  18. Sometimes when I'm just goofing off with math or science I notice weird things and think "there's no way someone hasn't discovered this yet" and just don't think about documenting my findings. this is what happens when every mathematician on the planet did that for 5000 years straight
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  19. 13:51 I count 54. Each 2D plane has 6: 4 small squares, 1 large square, and 1 diagonal square with corners at the midpoints of the edges. There are 3 of these planes in each orientation, and 3 × 3 × 6 = 54. Intuitively, I felt like there were also 6 more, each with two corners at the centres of opposite faces of the large cube, two corners at the midpoints of two of the edges that link those faces, and each side of the square being the long diagonal of a grid cube. It turns out these aren't actually squares, since one diagonal is √2 times longer than the other.
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  20. So much great content packed into 45 minutes! Something I’ll always remember will be that the no nines series converges, and how simple the proof was!
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  21. My non-mathematician intuition tells me that the Aztec diamond is some sort of parallell to how observable time is only able to move forwards, as colliding time cancels out and disappears. The four corners would be the 4 observable dimensions we live in. And; may the 4th be with you all as we travel inevitably into the year of 2021.
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  22. 9:03 On the last row, the 3rd and 6th are the same pattern. Blue-blue-yellow-blue seems to be missing, but so does blue-blue-yellow-yellow, so there must be another duplicate somewhere.
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  23. Something I like underpinning the two proofs is the duality of representations of triangles implicit in them. Three sides, or three angles and area. That one proof exists demands that the other one should be there as well. Nice.
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  24. 24:42 is not only a beautiful palindrome timestamp, but in a flash it gave me a deep understanding of both the Euclidian algorithm and of continued fractions. Thank you!
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  25. It's always beautiful how different fields of mathematics combine. Like geometry and linear algebra in this case.
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  26. I'm a simple man, I see mathologer video, i make popcorn and watch it!
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  27. That T-Shirt is quite harmonious 😃
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  28.  @dr.doppeldecker3832  Getting any of the concepts addressed on this channel into less than a minute would be impressive.
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  29. Love the shorter videos as well, keep'em coming 👍
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  30. Ein kürzeres Video von Zeit zu Zeit würde mich sehr freuen. Aber bitte keine "You Tube Shorts" LOL
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  31.  @jannikheidemann3805  There are Latin language classes available in some universities in the United States. But Latin Math class is not in the states!
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  32. "Just tell our brains to shut up." one of the nicest phrases concerning the understanding of math problems.
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  33. Welcome back! We missed you, mein Herr! Hertzlich willkommen!
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  34. i always wanted to dig into partitions but never got around to it. Thank you for outlying it and making it so easy to follow! Euler used to be my favourite as well, that dude was amazing. Good job Mathologer, keep it up
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  35. I have a special relationship to Ptomelys Inequality because it's the first theorem where I came up with an original and beautiful proof of it. And it was actually because of you :D Back then, I was re-watching some video about proofs of Pythagoras and one of the proofs involved scaling the original triangle by the factors a, b and c and then rearranging the parts in a clever way. You can do the same thing with Ptolemys Inquality! Take any quadrilateral with side lengths a, A, b, B, c, C like in your video but make sure that c is "in between" a and b. Take three copies of the quadrilateral and scale it by a, b and c respectively. Notice that two of your copies now have a side with length ab and diagonals ac and bc respectively. Join them on the side ab. Now notice that you can fit the third copy perfectly on the diagonals of the other two, as the third copy has two side lengths ac and bc too and the angle also matches. Put it in place and look carefully. You will have formed a triangle with side lengths aA, bB and cC. Ptolemys Inquality therefore follows. And the equality will hold exactly when the point lands exactly on the cC side. Which will happen exactly when the opposite angles of the original quadrilateral add up to 180 degrees which is exactly the case when it is circular. qed I stand by my opinion that this proof is absolutely marvelous and the best proof of Ptolemys Inequality ever. And it's perfect for an animation so if you ever want to show it, I absolutely allow you to do so :)
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  36. This video made my day,i was waiting eagerly for a mathologer video
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  37. Thanks. Based on the little I know about Chinese numerals, some of the ones shown seem to be being used in an Arabic way - e.g. 九八七 = 9 8 7, whereas I would expect it to be 九百八十七. Is that the point you were making?
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  38. What you noticed is essentially equivalent to the correct thing—we know that the right column turns out to be the sequence of numbers one less than a corresponding Fibonacci number. (Specifically R(i) = F(i+2) - 1) Because Fibonacci numbers have the add the last two to get the next relationship, adding R(i) = F(i+2) -1 and R(i+1) = F(i+3) - 1 gives F(i+4) - 2 and so adding one does give exactly F(i+4)-1 = R(i+2).
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  39. The Greedy algorithm has to be the most memorable. simple, yet brilliant
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  40. I was never taught the proof.
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  41. Is that the me Zachary Kaplan? Thats very exciting, if so! I really enjoyed this video; combinatorics is one of my favorite subjects, and the arguments used were very clever. Next up on my list is to really read about how that crazy monster formula for the square chessboards is derived!
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  42. But have you seen Vi Hart’s video on edible cyclides? (This one wasn’t a collab - just a coincidence.)
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  43. I remember learning that the volume of a sphere equals the volume of the respective cylinder minus that of the cone back in school, but it completely blew my mind to learn the equivalent is also true for a parabola. Also, it's amazing how the derivative of the volume of a shpere is its surface area. Made me realize how I've been taking things for granted withhout actually analyzing them. Thank you for providing me with all this insight! Keep making great videos like this!!
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  44. Marvelous content! The hidden theme of balancing the numbers around the mean itched my mind, but once I saw the solution I was in awe of the elegance of Bachet's algorithm. Can't wait to implement it in python.
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  45. As promised, I put the like also for this new version
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  46. At 12:00, why isn't 15 listed as divisor of 15, or 19 as divisor of 19?
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  47. 31:20 That magic moment when one needs to watch the Mathologer to finally understand where the abundance of "this is the way" memes is coming from all of a sudden...
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  48. Very interesting, thank you!
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  49. I think the number of tight lacings is (n!^2)/(2n). So that would be 1440 for n=5.
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  50. Thank you for introducing us to Peter Steinbach's work; your mission is accomplished! This has to be one of the most beautiful math lectures I've experienced. My eyes welled up when we got to the powers of phi, and I had to pause the video and go for a walk when I realized there's a Pascal triangle coming. Math (for me at least) can be overwhelmingly beautiful at times.
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