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Nonagon
In geometry, a nonagon () or enneagon () is a nine-sided polygon or 9-gon. The name ''nonagon'' is a prefix hybrid formation, from Latin (''nonus'', "ninth" + ''gonon''), used equivalently, attested already in the 16th century in French ''nonogone'' and in English from the 17th century. The name ''enneagon'' comes from Greek ''enneagonon'' (εννεα, "nine" + γωνον (from γωνία = "corner")), and is arguably more correct, though less common than "nonagon". Regular nonagon A '' regular nonagon'' is represented by Schläfli symbol and has internal angles of 140°. The area of a regular nonagon of side length ''a'' is given by :A = \fraca^2\cot\frac=(9/2)ar = 9r^2\tan(\pi/9) :::= (9/2)R^2\sin(2\pi/9)\simeq6.18182\,a^2, where the radius ''r'' of the inscribed circle of the regular nonagon is :r=(a/2)\cot(\pi/9) and where ''R'' is the radius of its circumscribed circle: :R = \sqrt=r\sec(\pi/9). Construction Although a regular nonagon is not constructible with com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polygon
In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two together, may be called a polygon. The segments of a polygonal circuit are called its '' edges'' or ''sides''. The points where two edges meet are the polygon's '' vertices'' (singular: vertex) or ''corners''. The interior of a solid polygon is sometimes called its ''body''. An ''n''-gon is a polygon with ''n'' sides; for example, a triangle is a 3-gon. A simple polygon is one which does not intersect itself. Mathematicians are often concerned only with the bounding polygonal chains of simple polygons and they often define a polygon accordingly. A polygonal boundary may be allowed to cross over itself, creating star polygons and other self-intersecting polygons. A polygon is a 2-dimensional example of the more general polytope in any number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hybrid Word
A hybrid word or hybridism is a word that etymologically derives from at least two languages. Common hybrids The most common form of hybrid word in English combines Latin and Greek parts. Since many prefixes and suffixes in English are of Latin or Greek etymology, it is straightforward to add a prefix or suffix from one language to an English word that comes from a different language, thus creating a hybrid word. Hybridisms were formerly often considered to be barbarisms., ''s.v.'' 'barbarism' English examples * Antacid – from Greek () 'against' and Latin acidus 'acid'; this term dates back to 1732. *Aquaphobia – from Latin 'water' and Greek () 'fear'; this term is distinguished from the non-hybrid word '' hydrophobia'', which can refer to symptoms of rabies. * Asexual – from Greek prefix 'without' and the Latin 'sex' * Automobile – a wheeled passenger vehicle, from Greek () 'self' and Latin 'moveable' * Beatnik – a 1950s counterculture movement centered on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
They Might Be Giants
They Might Be Giants (often abbreviated as TMBG) is an American alternative rock band formed in 1982 by John Flansburgh and John Linnell. During TMBG's early years, Flansburgh and Linnell frequently performed as a duo, often accompanied by a drum machine. In the early 1990s, TMBG expanded to include a backing band. The duo has been credited as vital in the creation and growth of the prolific DIY music scene in Brooklyn in the mid-1980s; the duo's current backing band consists of Marty Beller, Dan Miller and Danny Weinkauf. The group have been noted for their unique style of alternative music, typically using surreal, humorous lyrics, experimental styles and unconventional instruments in their songs. Over their career, they have found success on the modern rock and college radio charts. They have also found success in children's music with several educational albums, and in theme music for television programs and films. TMBG have released 23 studio albums. ''Flood'' has been ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
8-simplex T0
In geometry, an 8-simplex is a self-dual Regular polytope, regular 8-polytope. It has 9 vertex (geometry), vertices, 36 Edge (geometry), edges, 84 triangle Face (geometry), faces, 126 tetrahedral Cell (mathematics), cells, 126 5-cell 4-faces, 84 5-simplex 5-faces, 36 6-simplex 6-faces, and 9 7-simplex 7-faces. Its dihedral angle is cos−1(1/8), or approximately 82.82°. It can also be called an enneazetton, or ennea-8-tope, as a 9-facet (geometry), facetted polytope in eight-dimensions. The 5-polytope#A note on generality of terms for n-polytopes and elements, name ''enneazetton'' is derived from ''ennea'' for nine Facet (mathematics), facets in Greek language, Greek and Zetta, ''-zetta'' for having seven-dimensional facets, and ''-on''. As a configuration This Regular 4-polytope#As configurations, configuration matrix represents the 8-simplex. The rows and columns correspond to vertices, edges, faces, cells, 4-faces, 5-faces, 6-faces and 7-faces. The diagonal numbers say how man ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
8-simplex
In geometry, an 8-simplex is a self-dual regular 8-polytope. It has 9 vertices, 36 edges, 84 triangle faces, 126 tetrahedral cells, 126 5-cell 4-faces, 84 5-simplex 5-faces, 36 6-simplex 6-faces, and 9 7-simplex 7-faces. Its dihedral angle is cos−1(1/8), or approximately 82.82°. It can also be called an enneazetton, or ennea-8-tope, as a 9- facetted polytope in eight-dimensions. The name ''enneazetton'' is derived from ''ennea'' for nine facets in Greek and ''-zetta'' for having seven-dimensional facets, and ''-on''. As a configuration This configuration matrix represents the 8-simplex. The rows and columns correspond to vertices, edges, faces, cells, 4-faces, 5-faces, 6-faces and 7-faces. The diagonal numbers say how many of each element occur in the whole 8-simplex. The nondiagonal numbers say how many of the column's element occur in or at the row's element. This self-dual simplex's matrix is identical to its 180 degree rotation. \begin\begin 9 & 8 & 28 & 56 & 70 & ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthographic Projection
Orthographic projection (also orthogonal projection and analemma) is a means of representing Three-dimensional space, three-dimensional objects in Two-dimensional space, two dimensions. Orthographic projection is a form of parallel projection in which all the projection lines are orthogonal to the projection plane, resulting in every plane of the scene appearing in affine transformation on the viewing surface. The obverse of an orthographic projection is an oblique projection, which is a parallel projection in which the projection lines are ''not'' orthogonal to the projection plane. The term ''orthographic'' sometimes means a technique in multiview projection in which principal axes or the planes of the subject are also parallel with the projection plane to create the ''primary views''. If the principal planes or axes of an object in an orthographic projection are ''not'' parallel with the projection plane, the depiction is called ''axonometric'' or an ''auxiliary views''. (''A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complete Graph
In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph is a directed graph in which every pair of distinct vertices is connected by a pair of unique edges (one in each direction). Graph theory itself is typically dated as beginning with Leonhard Euler's 1736 work on the Seven Bridges of Königsberg. However, drawings of complete graphs, with their vertices placed on the points of a regular polygon, had already appeared in the 13th century, in the work of Ramon Llull. Such a drawing is sometimes referred to as a mystic rose. Properties The complete graph on vertices is denoted by . Some sources claim that the letter in this notation stands for the German word , but the German name for a complete graph, , does not contain the letter , and other sources state that the notation honors the contributions of Kazimierz Kuratowski to graph theory. has edges (a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conway Tiling DKH
Conway may refer to: Places United States * Conway, Arkansas * Conway County, Arkansas * Lake Conway, Arkansas * Conway, Florida * Conway, Iowa * Conway, Kansas * Conway, Louisiana * Conway, Massachusetts * Conway, Michigan * Conway Township, Michigan * Conway, Missouri * Conway, New Hampshire, a New England town ** Conway (CDP), New Hampshire, village in the town * Conway, North Dakota * Conway, North Carolina * Conway, Pennsylvania * Conway, South Carolina * Conway River (Virginia) * Conway, Washington Elsewhere * Conway, Queensland, a locality in the Whitsunday Region, Queensland, Australia * Conway River (New Zealand) * Conway, Wales, now spelt Conwy, a town with a castle in North Wales * River Conway, Wales, similarly respelt River Conwy Ships * HMS ''Conway'' (school ship) * HMS ''Conway'' (1832), a 26-gun sixth rate launched in 1832 * USS ''Conway'' (DD-70) or USS ''Craven'' (DD-70), a Caldwell class destroyer launched in 1918 * USS ''Conway'' (DD-507), a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetrohedron
In geometry, a symmetrohedron is a high-symmetry polyhedron containing convex regular polygons on symmetry axes with gaps on the convex hull filled by irregular polygons. The name was coined by Craig S. Kaplan and George W. Hart. The trivial cases are the Platonic solids, Archimedean solids with all regular polygons. A first class is called ''bowtie'' which contain pairs of trapezoidal faces. A second class has kite faces. Another class are called LCM symmetrohedra. Symbolic notation Each symmetrohedron is described by a symbolic expression G(l; m; n; α). G represents the symmetry group (T,O,I). The values l, m and n are the multipliers ; a multiplier of m will cause a regular km-gon to be placed at every k-fold axis of G. In the notation, the axis degrees are assumed to be sorted in descending order, 5,3,2 for I, 4,3,2 for O, and 3,3,2 for T . We also allow two special values for the multipliers: *, indicating that no polygons should be placed on the given axes, and 0, ind ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Directed Edge
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs. Definition In formal terms, a directed graph is an ordered pair where * ''V'' is a set whose elements are called '' vertices'', ''nodes'', or ''points''; * ''A'' is a set of ordered pairs of vertices, called ''arcs'', ''directed edges'' (sometimes simply ''edges'' with the corresponding set named ''E'' instead of ''A''), ''arrows'', or ''directed lines''. It differs from an ordinary or undirected graph, in that the latter is defined in terms of unordered pairs of vertices, which are usually called ''edges'', ''links'' or ''lines''. The aforementioned definition does not allow a directed graph to have multiple arrows with the same source and target nodes, but some authors consider a broader definition that allows directed graphs to have such multiple arcs (namely, they allow the arc set to be a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chaim Goodman-Strauss
Chaim Goodman-Strauss (born June 22, 1967 in Austin TX) is an American mathematician who works in convex geometry, especially aperiodic tiling. He is on the faculty of the University of Arkansas and is a co-author with John H. Conway of ''The Symmetries of Things'', a comprehensive book surveying the mathematical theory of patterns. Education and career Goodman-Strauss received both his B.S. (1988) and Ph.D. (1994) in mathematics from the University of Texas at Austin.Chaim Goodman-Strauss The College Board His doctoral advisor was . He joined the faculty at the |
