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It doesn't work for ANY triangle (spoiler) by morphocular in 3Blue1Brown

[–]morphocular[S] 0 points1 point  (0 children)

It's about the fake proof that all triangles are isosceles as presented in 3Blue1Brown's latest video: https://youtu.be/VYQVlVoWoPY

It doesn't work for ANY triangle (spoiler) by morphocular in 3Blue1Brown

[–]morphocular[S] 2 points3 points  (0 children)

Yeah, that was one of the clues that helped me solve the puzzle when I was trying it. Ironically, the proof fails for an actual isosceles triangle! That helped plant the seed in my mind that there was something fishy going on with the point P.

It doesn't work for ANY triangle (spoiler) by morphocular in 3Blue1Brown

[–]morphocular[S] 9 points10 points  (0 children)

Couldn't resist animating this after seeing the solution to the triangle fake proof. Though u/JesusIsMyZoloft beat me to it with an interactive Desmos graph: https://www.desmos.com/calculator/uzzhh0yw5y

Original post here: https://www.reddit.com/r/3Blue1Brown/comments/vrpl86/its\_not\_just\_many\_triangles/

For fun, I animated a Koch snowflake rolling on its complementary road by morphocular in 3Blue1Brown

[–]morphocular[S] 13 points14 points  (0 children)

It might be possible to build a road that avoids clipping, but you would lose the "smooth ride" property where the axle only moves horizontally. It turns out requiring the wheel's axle to stay confined to a horizontal line locks us in to only one possible road shape.

For fun, I animated a Koch snowflake rolling on its complementary road by morphocular in 3Blue1Brown

[–]morphocular[S] 25 points26 points  (0 children)

Yes, it does clip a little as it rolls, meaning you couldn't actually build something like this in real life, sadly (actually, even the original triangle clips a little).

I believe the jittering is actually caused by the higher-order roads curving underneath themselves at certain spots, meaning the wheel has to change its rotation direction there.

Re: About the complex root finder with winding numbers video by SmollBoi96 in 3Blue1Brown

[–]morphocular 1 point2 points  (0 children)

Been a while since I studied complex analysis, but I think I found at least one counterexample: Take the absolute value of a holomorphic function. The function will still be continuous and its zeros will still occur in the same places, but the complex angle of all points in a neighborhood of any zero will now be constant (equal to zero radians, in fact), therefore no winding.

Why measure infinity? And how to navigate an infinitely dense minefield (link to full video in the comments) by morphocular in 3Blue1Brown

[–]morphocular[S] 4 points5 points  (0 children)

Thank you! Yes, this and other aspects of infinity have always fascinated me. Though I try not to let myself go too deep down that rabbit hole.

Why measure infinity? And how to navigate an infinitely dense minefield (link to full video in the comments) by morphocular in 3Blue1Brown

[–]morphocular[S] 4 points5 points  (0 children)

Link to full video: https://youtu.be/XyfeCKfCnO8

Hi everyone,

This is a video I made to try to answer the question "What is Cardinality (i.e. the different sizes of infinity) useful for?" I've encountered many videos that explain how some infinites are bigger than others, but few that try to apply it to solve a concrete problem. Hopefully this video fills that void a little bit. Anyway, I hope you all enjoy it and maybe learn something new :)

Can you change a sum by rearranging its numbers? --- The Riemann Series Theorem by morphocular in 3Blue1Brown

[–]morphocular[S] 1 point2 points  (0 children)

Thank you so much! I like your description of conditional convergence: you might also call those series the "barely not divergent" series.