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Apeirogonal Tilings
In geometry, an apeirogonal tiling is a tessellation of the Euclidean plane, hyperbolic plane, or some other two-dimensional space by apeirogons. Tilings of this type include: *Order-2 apeirogonal tiling, Euclidean tiling of two half-spaces *Order-3 apeirogonal tiling, hyperbolic tiling with 3 apeirogons around a vertex *Order-4 apeirogonal tiling, hyperbolic tiling with 4 apeirogons around a vertex *Order-5 apeirogonal tiling, hyperbolic tiling with 5 apeirogons around a vertex *Infinite-order apeirogonal tiling, hyperbolic tiling with an infinite number of apeirogons around a vertex The vertices of an order-k apeirogonal tiling form a Bethe lattice, a regular infinite tree. See also *Apeirogonal antiprism *Apeirogonal prism *Apeirohedron References {{set index article, mathematics Apeirogonal tilings ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a ''List of geometers, geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point (geometry), point, line (geometry), line, plane (geometry), plane, distance, angle, surface (mathematics), surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, Wiles's proof of Fermat's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
