Ciro Santilli @cirosantilli 37

Points in the direction in which a wind spinner spins fastest.

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Continuous version of the Fourier series.

Can be used to represent functions that are not periodic: math.stackexchange.com/questions/221137/what-is-the-difference-between-fourier-series-and-fourier-transformation while the Fourier series is only for periodic functions.

Of course, every function defined on a finite line segment (i.e. a compact space).

Therefore, the Fourier transform can be seen as a generalization of the Fourier series that can also decompose functions defined on the entire real line.

As a more concrete example, just like the Fourier series is how you solve the heat equation on a line segment with Dirichlet boundary conditions as shown at: Section "Solving partial differential equations with the Fourier series", the Fourier transform is what you need to solve the problem when the domain is the entire real line.

A conjecture is an open problem in mathematics for which some famous dude gave heuristic arguments which indicate if the theorem is true or false.

Selected answers by Ciro Santilli on the subject:

The organic Usenet origins are quite hardcore!

Ideally can be thought of as a one-way ticket gate that only lets electrons go in one direction with zero resistance! Real devices do have imperfections however, so there is some resistance.

First they were made out of vacuum tubes, but later semiconductor diodes were invented and became much more widespread.

It sees and moves individual atoms!!!