Hearted Youtube comments on Mathologer (@Mathologer) channel.

  1. Wow, windmills! this is one straight from what Paul Erdős calls "the book" Now we know what Peter and Hanna really did in that windmill...
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  2. I figured out best solution for tower of hanoi when i was 6... My dad gave to me tower of hanoi puzzle with 8 peaces and so that i don't bother him said that i should find best solution and left me like that, and then was very surprised that 3 hours later i came to him and said "255", he already even forgot that he gave me the puzzle, but back in those days i figured out the recursive solution to tower of hanoi which impressed my father quite a bit... I was always good with recursive algorithms...
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  3. Nice vid’ bro
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  4. Wow. Just wow.
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  5. I see an immediate application of this theory. It could be used in power system engineering. The three-phase voltages and currents for any imbalanced system could be broken down into three balanced components. The first balanced component would represent positive rotational torque, the second component would represent a negative rotational torque, and the third component would represent a non rotational component. Since these components are themselves balanced we could call this idea Symmetrical Sequence Components. You can take the transformation matrix shown in the video at 27:30 and create a 3x3 version of this to use for three-phase systems - but it would be good to change the Greek letter used for the rotational operator to the small letter alpha and then try and come up with a catchy name for this 3x3 transform. Could I suggest that we call it a Fortescue Transform and back date it to 1918.
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  6. 23:09 Turn on subtitles here
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  7. I was taught Heron's formula in Belgian high school. 12th grade, the most intensive math option they had (8 hours/week). And only as a side tangent, without proof.
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  8. One thing I noticed is that for example at 24:35 you need the fact that those two segments intersect each other. I don't know if that's something you can assume or you need a proof of that.
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  9. "just" 😅
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  10. This reminded me of my Calculus classes back in University... I have master degree in physics, which required a lot of calculus class... The only thing that this introduced to me (or maybe i have just already forgotten) is the source of Bernoulli numbers... But approximation you showed in the end was not new to me... I wasn't required to know it for exam but we were introduced to it in passing... I just like your explanations that is why i was watching... Not for new stuff but for new insights into stuff i more or less already known so far... A different angle you take to show known mathematical results is super awesome...
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  11. I made it to the very end. Partitions are amazing. My first introduction to them was through Ferrer diagrams and then later again with generating functions. It was nice to see yet another connection with pentagonal numbers. That one was new to me.
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  12. concerning the one-liner: f(x) = 1/x => 1/c * f(x * c) = 1/c * c/x = 1/x Q.E.D.
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  13. This algebra seems a little abstract... amirite?
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  14. Very sad to say that he is not very well known ... Even if you ask maths graduate in India there is a great chance that he never heard of his name...
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  15. Your videos are a marvel to behold (and dim memories of school learnings sometimes flit into view, briefly).
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  16.  @Θρησκόληπτος  I'm brazilian and Bolsonaro (alias BOZOnaro) is really a nightmare: incompetent and evil. Unfortunatelly, part of the population (decreasing everyday) still supports him.
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  17. base 10 haters will notice this works in any base :)
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  18. Really appreciate the perspective of a determinant as a sum of permutations, I've never seen that before. I feel like an actual intuition for the determinant may not be too far behind. Trace has been similarly confusing for me my whole life - what possible simple interpretation could it have, and why is it so conserved?
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  19.  @want-diversecontent3887  2x is cheating because you skip half the frames
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  20. I'm not the most mathematically trained or clever person, so I don't know if it was subtly covered in the video and I didn't catch it, but I noticed that the 4k+1 primes (Pythagorean primes as it turns out?) are all hypotenuses of pythagorean triples, that is, a^2+b^2=c^2, where a and b are integers and c is the pythagorean prime, or a 4k+1 prime. So, the pythagorean primes can be written as the sum of two integer squares, and the square of the pythagorean primes can be written as the sum of two integer squares. This is I guess part of the definition of a pythagorean prime, as well as being a prime of the form 4k+1. Is this totally obvious from what the video was about?
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  21. In hindsight, I saw my math teacher was showing us some of the math-related to famous anecdotes, like the sum 1..100 and also Collatz conjecture. Without ever mentioning it. As a planted memory, that might be a reminder. I like my math teacher very much. He was an Egyptian, and though he wasn't our main "Tutor" teacher, he invited the Leistuingskurs home and showed us a way to make a sweet (Mr. Tom) with peanuts and sugar sirup ourselves, without going to a shop in the school breaks and leave the school area, which actually was forbidden. I got the idea to group 1+100,2,+99, too. It's not that far fetched to get this idea. But powers is another story. But thanks for another reminder of a great time in school.
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  22. I think the transformation of the hollow space within the claw's sphere-like configuration would be interesting to see in animation too. Just off the top of my head, I believe it should correspond to the divets between the lunes in the disc-like configuration, but I've no solid proof for that right now
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  23. So where is 0? Actually I realized before 5 years that 0 has the same digital properties as 9. in general, in vortex-based mathematics, the first and the last number in any numaric system have the same propeties, So 9 is not special, it just happened to be the last digit in our number system.
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  24. Came for a fractal that looks like an iris, stayed for the beautiful visual geometric proofs
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  25. Dear Mathologer, Karl and Lara, thanks for this new year's gift! 🎁 Have a great year. 😀
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  26. Perfection deserves attention...
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  27. ​ @JackDraak  The E6B was just a specialized circular slide rule, of which there were many. About 50 years ago, you could get them as promotional material to calculate things relevant to your industry like concrete volumes or resistor sizes. Still a lot of interesting ones on ebay.
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  28. I'm a mandala artist and I find this fascinating. I've been creating eggs before the chicken... :-) Geometry has always been a passion of mine and I thank my high school teacher Mrs. Locke for making geometry interedting and thank you to you too for expanding my understanding !
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  29. Hahaha, i figured it out :)
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  30. I tried to watch all the way to the end; but first I had to watch halfway to the end, and then half of what was remaining, and then half of that, and then my friend Zeno texted me and we went and got pizza. (We're still trying to divide up the bill.)
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  31. You here use some magic to put this video together so nicely! 😍
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  32. Es un placer ver, escuchar y entender! Muy bien logrado Mathloger! 👍 Esperamos el próximo. 😀
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  33. 7:22 Proof Commutative Law for any Z/n: Since Z/n is just Z mod n for any whole number, we just have to add a+b and divide by n, then take the remainder, and that's our answer. Let C be the sum of a and b. But no matter what order you add whole numbers a and b, you always get the same number C by the ordinary commutative law of addition. So you will divide the same number by n no matter what order you add a and b in. Distributive Law for Z/n: The argument is basically the same, except you use the ordinary Distributive Law. You get the same number, which we will now call D, on each side of that second equation, so you will always be doing the operation D/n. This completes my proof for any modular ring Z/n being valid for both equations. QED. Let me know of there is any error in this logic.
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  34. Most times I take him for granted but damn... Euler was an absolute genius. Imagine if he never existed. We'd probably be at least 100 years less advanced mathematically
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  35. Ooooooo, nice thought, I'll have to verify. Well played mate.
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  36. I actually find the optimal stack of books quite aesthetically pleasing
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  37. @ Ohh that's fair. I guess I'm thinking of interacting with them as a colleague when I think back to being a student there were certainly profs who resisted admitting they were wrong to students.
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  38. u bet I am
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  39. ([π]-1)st comment
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  40. I found the constant by multiplying the side by the midpoint number. A 33x33 magic square has 1089 squares, the midpoint is 1089 divided by 2 rounded up: 545. So 545x33 (using this method of creating magic squares leaves the midpoint number in the middle of the square also), is 17985.
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  41. As one does
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  42. As always sir, I appreciate the free Educational Videos. You are keeping the love for Numbers alive.
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  43. not in a mathologer video
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  44. Everything is coincidence. It's just your brain that feels the need to give you the illusion that it's otherwise.
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  45. Funny, I just answered a Numberphile vid on Grandi, where they ask what's the answer .. I wrote an explanation with equations why no unique sum could exist.. the partial sums would always differ by one Now I could just refer them here
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  46. ​ @Wecoc1 wait really?
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  47. 2019 is in pi. AMAZING
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  48. just recently got a C in calculus 2…
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  49. Crazy, how unintuitive things can get
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  50.  @Mathologer  thats the tragedy , i do not want to be political , but the British as well as the islamic invasions wiped out a lot of ancient knowledge . for example the burning of Nalanda University whose Library burnt for 40 days and several manuscripts were burnt. This happened two hundered years before Madhava
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