@JonnElledge
[…Continued]
There are loads of resources on the WWW that do this far better justice, with more detail and less handwaving that I'm using here. There are also scads of pop science explanations by actual maths teachers. #Numberphile has #HannahFry discussing this with orange peel, for example. @standupmaths has probably covered it somewhere.
You'll know that you've reached the good stuff, the stuff that mathematicians and theoretical physicists deal in (knowing about intrinsic measure of curvature being necessary for a proper understanding of curved spacetime in General Relativity), when you come across the explanations that blithely throw in Christoffel symbols and Ricci tensors as if you know what the Hell they are on about. (-:
#maths #physics #Gauss #curvature