David Moore

Newton's shell theorem or Gauss's law! Make flashcards about it right away! This is a case where the indefinite integrals involved are way more complicated than the final result. There are some cases where you do have to wrestle with integrals like this though, so your work isn't in vain. Volume element is wrong, you either want x=r*[sin(theta) cos(phi), sin(theta)sin(phi), cos(theta)] and volume element r^2 sin(theta) dr dtheta dphi, with an integral from theta=0 to pi, phi=0 to 2 pi. Or you can choose x=r*[cos(theta) cos(phi), cos(theta)sin(phi), sin(theta)] but the volume element will be r^2 cos(theta) dr dtheta dphi and the integral should be taken taken from theta=-pi/2 to pi/2 to cover the whole sphere. With this coordinate stuff fixed, the integral *is* doable, though a bit annoying. This amounts to re-proving Newton's shell theorem though, so you can be proud of yourself for re-deriving Newton's work using modern methods :) (Physics teacher's assistant powers kicking in)

Where I'm at right now, will certainly add more books by the end of the month.

🥳

Automated proof checking language .mm files, not a general purpose database. Metamath is old-but-gold youtube.com/watch?v=OOF4NWRy…

There is something deeply, deeply funny to me about the way metamath databases look. "Yes, hi there, wrel, cdm, wss, oh and ACZADFBEZAHZABIUC"

oh boy almost math time

Woo. 's alright. I held back from doing too many back and forths. mathandcode.com/share/11-05-…

Oh interesting. Yeah for my particular post I meant to emphasize it was my own misconception, not an answer to your original question. I can't give a high confidence answer, it sounds like a cool question. I guess, wouldn't the Taylor series info in some coordinate patch live in the symmetric product of cotangent spaces? Since it's a sum like the following picture (f_{,i} = \partial_i f(x) evaluated at x=0). I think if I tried to get to the bottom of it I'd end up responding to things that are ultimately the mistakes of the translation software, maybe I already have! 😆 but it's fun to think about

Read 'em and weep, I now have a monopoly on Vampire Weekend parody songs about learning Metamath.

Who's gonna tell him...

Going over quiz questions from college. Back when I was learning mechanics I'd have done 8 pages of explicit matrix garbage to answer this, now it's like "oh yeah there's a commutator and it's simple once you diagonalize." This was a quals flashcard I quite like.