Stokes’ theorem. Almost the same thing as the high school one. It generalizes the fundamental theorem of calculus to arbitrary smooth manifolds. In the case that M is the interval [a, x] and ω is the differential 1-form f(t)dt on M, one has dω = f’(t)dt and ∂M is the oriented tuple {+x, -a}. Integrating f(t)dt over a finite set of oriented points is the same as evaluating at each point and summing, with negatively-oriented points getting a negative sign. Then Stokes’ theorem as written says that f(x) - f(a) = integral from a to x of f’(t) dt.
It’s the most general form of Stokes’ theorem that the integral of a differential form over the boundary of an volume and the integral of an exterior derivative of this form over that volume are the same. It covers a lot of classic formulas from the fundamental theorem of calculus to Green’s theorem, Gauss’ theorem and classic Stokes’ theorem.
The funny thing is as long as you have a small kid with you - doesn’t even have to be a baby, just stroller-age - you can bring anything. I’m not even talking about a sealed bottle of water - which, to me, would kind of make sense with the regulations - but all of the sudden your normal 500ml bottle with water, juice, or whatever, is fine. A thermo can with boiling hot water inside? Sure, no problem.
People who run the bots know that errors and misspellings create more interaction and include it in the automated posts, it also makes it seem less like a bot. There is more incentive for people who run bots to include these things than not to.
One of my favorite college courses was entirely on tribal art. I had no idea on the diversity in mask design and materials within tribes of the same region. I still have the book from it, the symbolism of it all is so neat. These people were as creative as we are.
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