me: show that as the number of dimensions increases, the ratio between the volume of an n-dimensional sphere & an n-dimensional cube approaches 0 my students: https://twitter.com/turing_police/status/1138945095749627905 …
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Replying to @georgiamarxist
That’s just because the volume of an n dimensional sphere goes to zero
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Replying to @InertialObservr
haha yeah that's true i was just trying to formulate a tweet real quick that referenced turing's :p though less advanced students could guess what'll happen by comparing 2d, then 3d, ... & seeing the ratio getting smaller. i wanna say ive seen that somewhere but can't remember
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Replying to @georgiamarxist
〈 Berger | Dillon 〉 Retweeted 〈 Berger | Dillon 〉
maybe it was one of my previous tweets ;)https://twitter.com/InertialObservr/status/1124078729809072131?s=20 …
〈 Berger | Dillon 〉 added,
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Replying to @InertialObservr
i think i am remembering some other more elementary context but that's incredibly beautiful what you just linked to, how have i never seen/noticed this before?!
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Not sure.. I was just looking at the wikipedia page and was like huh.. if I sum over that its e^π.. i hadn't seen it before that either
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If you sum over the volumes of all 2k-dimensional unit spheres, that sum converges to e^π.
I have no idea why this should be true..