The Fourier transform takes an input function f (in red) in the “time domain” and converts it into a new function f-hat (in blue) in the “frequency domain”.
In other words, the original function can be thought of as being “amplitude given time”, and the Fourier transform of the function is “amplitude given frequency”.
Shown here, a simple 6-component approximation of the square wave is decomposed (exactly, for simplicity) into 6 sine waves. These component frequencies show as very sharp peaks in the frequency domain of the function, shown as the blue graph. In practice, these peaks are never that sharp. That would require infinite precision.
I’m not too happy with this one yet. It’s a bit of a mixture of Fourier series and Fourier transform. The animation could also be a bit smoother in some steps. I may tweak it later.
The two-dimensional analogue of a polychoron is a polygon, and the three-dimensional analogue is a polyhedron. The term polychoron (plural polychora), from the Greek roots poly (‘many’) and choros (‘room’ or ‘space’) and has been advocated by Norman Johnson and George Olshevsky, but it is little known in general polytope theory. Other names for polychoron include: polyhedroid and polycell.
“Is the greater body of Stanley Kubrick’s films an exposé of a hidden elite obsessed with dark Saturnian sexual rites, paedophilia and the planned ritualistic transmutation of mankind?”
2001: A Space Odyssey: Kubrick’s undoubted masterpiece and at the centre of Jay Weidner’s alchemical take on Kubrick’s films. As discussed above, Weidner claims this film to be Kubrick’s attempt at an initiation rite of passage illustrating humanity’s next planned-for evolutionary step. Weidner believes Kubrick has revealed an occult agenda to launch us as a species into space where we will be able to embrace our destiny as future star children and join the greater cosmos.