Comments by "" (@zachrodan7543) on "3Blue1Brown" channel.

  1.  @AriKnits  you missed jaunt. it goes position, velocity, acceleration, jerk, jaunt, snap, crackle, pop
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  2. 18:48 who's on first
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  3. my personal preference for visualizing gradients is not a ball rolling down a hill, but cows trying to find the top of a hill in a flooded field... blame my calc 4 teacher. he was exceptionally good at explaining math
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  4. Two questions: 1. Does the inscribed rectangle theorem hold true for curves that are not embedded in a plane? And 2: pretty sure some of the curves in your montage of "smooth curves" to show how rectangles of any aspect ratio could be found in the case of smooth curves, were not smooth: the christmas tree and pi clearly had points where the derivative would be undefined.
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  5. love the idea of splitting up the chain rule step into two different things at 2:37. I know you were bringing this up as something that felt confusing when you first learned it, but for me, and for the students that I tutor, we are told to just remember to do the chain rule when taking the derivative of the pieces with y in them; I will often suggest to also throw a dx/dx next to the stuff with x, just as a reminder to do the chain rule in general, but the idea of just multiplying the derivatives of the things with x in them by dx, and the stuff with y by dy, and then afterwards dividing everything by dx, feels like it could potentially make the process a bit easier to follow for some students
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  6. spoilers for the "homework problem"... or at least, my response to it. I mean, of course anything that works for polynomials will work for integers. a polynomial is basically just a number in an unknown base. (342=3x^2+4x+2, where x=10)
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  7. how do complex seed values behave with repeated iterations of 1+1/z? do they also gravitate towards phi? or do some of them manage to get elsewhere?
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  8. thank you for making this video. I now have a much better appreciation for why complex numbers show up in so many weird places: it allows us to encode for periodicity in a simple, "complex" way
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  9. 7:18 that reminds me of a joke I made with one of the students I tutor: if the transition to symbolic mathematical notation happened today, we would be using emoji for variables
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  10. Thoughts on these puzzles: 1: no. Since the first tiling presented has no hexagons to rotate, you cannot get to or from it from any other tiling. This is not even the only tiling with no hexagons to rotate, as if you took that and flipped alternating columns you would get a tiling made of stacked chevrons, again, no hexagons to rotate. 1b: not sure, but i do notice that the number of tiles in each orientation is constant, so if there exists tilings with different numbers of pieces in each orientation, they would form separate equivalence classes, which you could not transfer between. I do not have the energy right now to contemplate the finer details. 2. The minimum sum should be the diameter of the circle. The optimal way to cover the circle with strips would be to lay strips side by side, with no overlap. Thus the sums of the widths must be at least the diameter.
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  11. 0:28 I often will joke that limits are arguably one of the most intuitive concepts in calculus, or possibly even in all of math: so much so that newton and liebniz were able to manage to explain calculus without bothering to formally define limits (which, like proving that 1+1=2, is a whole lot of effort just to convince people of something they probably already knew intuitively)
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  12. Where does the idea that the observable universe is about 20% of the entire universe come from? I would have thought that would depend on whether the universe was even finite to begin with, which was then dependent on the overall curvature of the universe, which we didn't quite have the tools to measure, as I understood it...
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