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  2. Quasicrystal - Wikipedia

    en.wikipedia.org/wiki/Quasicrystal

    The concept of an almost periodic function (also called a quasiperiodic function) was studied by Bohr, including work of Bohl and Escanglon. [47] He introduced the notion of a superspace. Bohr showed that quasiperiodic functions arise as restrictions of high-dimensional periodic functions to an irrational slice (an intersection with one or more ...

  3. Quasiperiodicity - Wikipedia

    en.wikipedia.org/wiki/Quasiperiodicity

    Quasiperiodic behavior is almost but not quite periodic. [2] The term used to denote oscillations that appear to follow a regular pattern but which do not have a fixed period. The term thus used does not have a precise definition and should not be confused with more strictly defined mathematical concepts such as an almost periodic function or a ...

  4. Quasiperiodic function - Wikipedia

    en.wikipedia.org/wiki/Quasiperiodic_function

    Bloch's theorem says that the eigenfunctions of a periodic Schrödinger equation (or other periodic linear equations) can be found in quasiperiodic form, and a related form of quasi-periodic solution for periodic linear differential equations is expressed by Floquet theory. Functions with an additive functional equation

  5. Tessellation - Wikipedia

    en.wikipedia.org/wiki/Tessellation

    One class that can be generated in this way is the rep-tiles; these tilings have unexpected self-replicating properties. [36] Pinwheel tilings are non-periodic, using a rep-tile construction; the tiles appear in infinitely many orientations. [37] It might be thought that a non-periodic pattern would be entirely without symmetry, but this is not so.

  6. Trigonometry - Wikipedia

    en.wikipedia.org/wiki/Trigonometry

    Fourier discovered that every continuous, periodic function could be described as an infinite sum of trigonometric functions. Even non-periodic functions can be represented as an integral of sines and cosines through the Fourier transform. This has applications to quantum mechanics [64] and communications, [65] among other fields.

  7. Periodic function - Wikipedia

    en.wikipedia.org/wiki/Periodic_function

    A periodic function, also called a periodic waveform (or simply periodic wave), is a function that repeats its values at regular intervals or periods. The repeatable part of the function or waveform is called a cycle . [ 1 ]

  8. Fourier series - Wikipedia

    en.wikipedia.org/wiki/Fourier_series

    Fig 1. The top graph shows a non-periodic function () in blue defined only over the red interval from 0 to P. The function can be analyzed over this interval to produce the Fourier series in the bottom graph. The Fourier series is always a periodic function, even if original function () is not.

  9. List of periodic functions - Wikipedia

    en.wikipedia.org/wiki/List_of_periodic_functions

    This is a list of some well-known periodic functions. The constant function f (x) = c, where c is independent of x, is periodic with any period, but lacks a fundamental period. A definition is given for some of the following functions, though each function may have many equivalent definitions.

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