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The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled, e.g., the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two directions.
In plane geometry, the einstein problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles; that is, a shape that can tessellate space but only in a nonperiodic way. Such a shape is called an einstein, a word play on ein Stein, German for "one stone". [2]
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]
An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic regions or patches. A set of tile-types (or prototiles) is aperiodic if copies of these tiles can form only non-periodic tilings. The Penrose tilings are a well-known example of aperiodic tilings. [1] [2]
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The term can also be used for non-periodic or aperiodic signals, like chirps and pulses. [3] In electronics, the term is usually applied to time-varying voltages, currents, or electromagnetic fields. In acoustics, it is usually applied to steady periodic sounds — variations of pressure in air or other media.
Place {{Anatomy terms}} in the "See also" section of the article. The above documentation is transcluded from Template:Anatomy terms/doc . ( edit | history )
Anatomy is a branch of morphology that deals with the structure of the body at a level higher than tissue. [3] Anatomy is closely related to histology, which studies the structure of tissues, as well as cytology, which studies the structure and function of the individual cells, from which the tissues and organs of the studied macroorganism are ...