/sci/ - Science & Math

>>14769821
>>14769875
Wait do you mean analytic geometry as in coordinate geometry?
I think the analytic there comes from the same analytic used in analytic philosophy, so it's meaningless for all practical purposes.

>>14727952
>then f must vanish everywhere on [0,2π] except on a set of measure zero.
You've instantly lost me with your proof.

>>14709303
The latter.
>Why do they show us this stuff when we're learning it for the first time?
So you can actually understand things without just knowing them by heart.
>>14710424
>How can an optimizer do worse with jacobians than without jacobians?
Shit man the geometry behind this is too basic to actually explain.
A non-constrained problem can go straight to the minimum, a constrained problem can take retarded, tortuous paths.
Or vice versa.
>>14711837
>Does there exist a scale (like for measuring mass) precise enough to detect a beam of light shining onto it?
IIRC the fact that light could cause measurable force was part of Einstein's empirical evidence for relativity and for light having momentum in spite of having no mass.
>>14711785
>it encodes the same information as homology
It doesn't necessarily.
But if I had to give a single main point then it's "cohomology ring".