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Ammann–Beenker Tiling
In geometry, an Ammann–Beenker tiling is a nonperiodic tiling which can be generated either by an aperiodic set of prototiles as done by Robert Ammann in the 1970s, or by the cut-and-project method as done independently by F. P. M. Beenker. They are one of the five sets of tilings discovered by Ammann and described in ''Tilings and Patterns''. The Ammann–Beenker tilings have many properties similar to the more famous Penrose tilings: *They are nonperiodic, which means that they lack any translational symmetry. *Their non-periodicity is implied by their hierarchical structure: the tilings are substitution tilings arising from substitution rules for growing larger and larger patches. This substitution structure also implies that: *Any finite region (patch) in a tiling appears infinitely many times in that tiling and, in fact, in any other tiling. Thus, the infinite tilings all look similar to one another, if one looks only at finite patches. *They are quasicrystalline: implemen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pell Number
In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins , , , , and , so the sequence of Pell numbers begins with 1, 2, 5, 12, and 29. The numerators of the same sequence of approximations are half the companion Pell numbers or Pell–Lucas numbers; these numbers form a second infinite sequence that begins with 2, 6, 14, 34, and 82. Both the Pell numbers and the companion Pell numbers may be calculated by means of a recurrence relation similar to that for the Fibonacci numbers, and both sequences of numbers grow exponentially, proportionally to powers of the silver ratio 1 + . As well as being used to approximate the square root of two, Pell numbers can be used to find square triangular numbers, to construct integer approximations to the right isosceles triangle, and to solve certain combinat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tesseract
In geometry, a tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells. The tesseract is one of the six convex regular 4-polytopes. The tesseract is also called an 8-cell, C8, (regular) octachoron, octahedroid, cubic prism, and tetracube. It is the four-dimensional hypercube, or 4-cube as a member of the dimensional family of hypercubes or measure polytopes. Coxeter labels it the \gamma_4 polytope. The term ''hypercube'' without a dimension reference is frequently treated as a synonym for this specific polytope. The ''Oxford English Dictionary'' traces the word ''tesseract'' to Charles Howard Hinton's 1888 book ''A New Era of Thought''. The term derives from the Greek ( 'four') and from ( 'ray'), referring to the four edges from each vertex to other vertices. Hinton originally spell ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tesseractic Honeycomb
In four-dimensional euclidean geometry, the tesseractic honeycomb is one of the three regular space-filling tessellations (or honeycombs), represented by Schläfli symbol , and constructed by a 4-dimensional packing of tesseract facets. Its vertex figure is a 16-cell. Two tesseracts meet at each cubic cell, four meet at each square face, eight meet on each edge, and sixteen meet at each vertex. It is an analog of the square tiling, , of the plane and the cubic honeycomb, , of 3-space. These are all part of the hypercubic honeycomb family of tessellations of the form . Tessellations in this family are Self-dual. Coordinates Vertices of this honeycomb can be positioned in 4-space in all integer coordinates (i,j,k,l). Sphere packing Like all regular hypercubic honeycombs, the tesseractic honeycomb corresponds to a sphere packing of edge-length-diameter spheres centered on each vertex, or (dually) inscribed in each cell instead. In the hypercubic honeycomb of 4 dimensions, verte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ammann Bar
Ammann is a surname of German origin which is an alternative spelling of Amtmann or Amman, an historical kind of bailiff. Notable people with the surname include: *Alberto Ammann, Argentine actor *Daniel Ammann, Swiss author and journalist (born 1973) *Erwin Ammann, German politician and co-founder of the Christian Social Union of Bavaria (1916 – 2000) *Gretel Ammann (1947–2000), Spanish philosopher, writer and activist *Jakob Ammann, Swiss anabaptist leader and founder of the Amish (c. 1644 – c. 1730) *Johann Conrad Ammann, Swiss physician and fossil collector (1724 – 1811) *Johann Konrad Ammann, Swiss physician and instructor of deaf persons (1669 – 1724) *Johann Schneider-Ammann, Swiss politician (born 1952) *Mike Ammann, American soccer player (born 1971) *Othmar Ammann, structural engineer who built many of New York City's bridges (1879 – 1965) *Robert Ammann, American amateur mathematician with contributions to aperiodic tilings (1946 – 1994) *Simon Ammann, Swiss ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ammann Bars
Ammann is a surname of German origin which is an alternative spelling of Amtmann or Amman, an historical kind of bailiff. Notable people with the surname include: *Alberto Ammann, Argentine actor *Daniel Ammann, Swiss author and journalist (born 1973) *Erwin Ammann, German politician and co-founder of the Christian Social Union of Bavaria (1916 – 2000) *Gretel Ammann (1947–2000), Spanish philosopher, writer and activist *Jakob Ammann, Swiss anabaptist leader and founder of the Amish (c. 1644 – c. 1730) *Johann Conrad Ammann, Swiss physician and fossil collector (1724 – 1811) *Johann Konrad Ammann, Swiss physician and instructor of deaf persons (1669 – 1724) *Johann Schneider-Ammann, Swiss politician (born 1952) *Mike Ammann, American soccer player (born 1971) *Othmar Ammann, structural engineer who built many of New York City's bridges (1879 – 1965) *Robert Ammann, American amateur mathematician with contributions to aperiodic tilings (1946 – 1994) *Simon Ammann, Swiss ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
