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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. List of aperiodic sets of tiles - Wikipedia

    en.wikipedia.org/wiki/List_of_aperiodic_sets_of...

    An example of such a tiling is shown in the adjacent diagram (see the image description for more information). A tiling that cannot be constructed from a single primitive cell is called nonperiodic. If a given set of tiles allows only nonperiodic tilings, then this set of tiles is called aperiodic . [ 3 ]

  4. 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.

  5. 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.

  6. List of mathematical functions - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_functions

    Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.

  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. Trapezoidal rule - Wikipedia

    en.wikipedia.org/wiki/Trapezoidal_rule

    The trapezoidal rule converges rapidly for periodic functions. This is an easy consequence of the Euler-Maclaurin summation formula , which says that if f {\displaystyle f} is p {\displaystyle p} times continuously differentiable with period T {\displaystyle T} ∑ k = 0 N − 1 f ( k h ) h = ∫ 0 T f ( x ) d x + ∑ k = 1 ⌊ p / 2 ⌋ B 2 k ...

  9. 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.