Trilemmas are everywhere. Defined as either a forced single choice among three unfavorable options or a two-out-of-three-only choice among favorable options, trilemmas involve trade-offs. The latter, ...

Get an easy, step-by-step explanation of the Gauss Divergence Theorem designed to make this important vector calculus concept ...

Determining which configurations of the cube are possible. The Fundamental Theorem of Cubology is a statement that characterizes which configurations are possible, and which configurations are ...

This is a preview. Log in through your library . Abstract The Serre duality for a holomorphic vector bundle over a compact, complex manifold still holds over a compact, strongly pseudo-convex manifold ...

In the context of Lebesgue integration, we derive the divergence theorem for unbounded vector fields that can have singularities at every point of a compact set whose Minkowski content of codimension ...

Many prominent phenomena originate from geometrical effects rather than from local physics. For example, the 'hairy ball' (HB) theorem asserts that a hairy sphere cannot be combed without introducing ...

The Hairy Ball theorem, proved by Henri Poincaré in 1885, demonstrates that it's impossible to create a perfectly smooth hair ...

You might be surprised to learn that you can’t comb the hairs flat on a coconut without creating a cowlick. Perhaps even more surprising, this silly claim with an even sillier name, the “hairy ball ...