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Spirolateral
In Euclidean geometry, a spirolateral is a polygon created by a sequence of fixed vertex internal angles and sequential edge lengths 1,2,3,...,''n'' which repeat until the figure closes. The number of repeats needed is called its cycles. Gardner, M. ''Worm Paths'' Ch. 17 ''Knotted Doughnuts and Other Mathematical Entertainments'' New York: W. H. Freeman, pp. 205-221, 1986/ref> A ''simple spirolateral'' has only positive angles. A simple spiral approximates of a portion of an archimedean spiral. A ''general spirolateral'' allows positive and negative angles. A ''spirolateral'' which completes in one turn is a simple polygon, while requiring more than 1 turn is a star polygon and must be self-crossing. A simple spirolateral can be an equangular simple polygon with ''p'' vertices, or an equiangular star polygon with ''p'' vertices and ''q'' turns. Spirolaterals were invented and named by Frank C. Odds as a teenager in 1962, as ''square spirolaterals'' with 90° angles, drawn on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Spirolateral 3 90
In Euclidean geometry, a spirolateral is a polygon created by a sequence of fixed vertex internal angles and sequential edge lengths 1,2,3,...,''n'' which repeat until the figure closes. The number of repeats needed is called its cycles.Martin Gardner, Gardner, M. ''Worm Paths'' Ch. 17 ''Knotted Doughnuts and Other Mathematical Entertainments'' New York: W. H. Freeman, pp. 205-221, 1986/ref> A ''simple spirolateral'' has only positive angles. A simple spiral approximates of a portion of an archimedean spiral. A ''general spirolateral'' allows positive and negative angles. A ''spirolateral'' which completes in one Turn (geometry), turn is a simple polygon, while requiring more than 1 turn is a star polygon and must be self-crossing. A simple spirolateral can be an equangular simple polygon with ''p'' vertices, or an equiangular star polygon with ''p'' vertices and ''q'' turns. Spirolaterals were invented and named by Frank C. Odds as a teenager in 1962, as ''square spirolaterals' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Golygon
A golygon, or more generally a serial isogon of 90°, is any polygon with all right angles (a rectilinear polygon) whose sides are consecutive integer lengths. Golygons were invented and named by Lee Sallows, and popularized by A.K. Dewdney in a 1990 ''Scientific American'' column (Smith). Variations on the definition of golygons involve allowing edges to cross, using sequences of edge lengths other than the consecutive integers, and considering turn angles other than 90°. Properties In any golygon, all horizontal edges have the same parity as each other, as do all vertical edges. Therefore, the number ''n'' of sides must allow the solution of the system of equations :\pm 1 \pm 3 \pm \cdots \pm (n-1) = 0 :\pm 2 \pm 4 \pm \cdots \pm n = 0. It follows from this that ''n'' must be a multiple of 8. For example, in the figure we have -1 + 3 + 5 - 7 = 0 and 2 - 4 - 6 + 8 = 0. The number of golygons for a given permissible value of ''n'' may be computed efficiently using generating ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Star Polygon
In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not to have been formally defined, Decagram (geometry)#Related figures, certain notable ones can arise through truncation operations on regular simple or star polygons. Branko Grünbaum identified two primary usages of this terminology by Johannes Kepler, one corresponding to the regular star polygons with List of self-intersecting polygons, intersecting edges that do not generate new vertices, and the other one to the isotoxal Concave polygon, concave simple polygons.Grünbaum & Shephard (1987). Tilings and Patterns. Section 2.5 Polygram (geometry), Polygrams include polygons like the pentagram, but also compound figures like the hexagram. One definition of a ''star polygon'', used in turtle graphics, is a polygon having ''q'' ≥ 2 Turn (geometry), turns (''q'' is called the turning number or Density (polygon), density), like in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
