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Spirolateral 1-12-3432 60
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 gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
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 f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turn Angle
In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or non-convex, this angle is called an interior angle (or ) if a point within the angle is in the interior of the polygon. A polygon has exactly one internal angle per vertex. If every internal angle of a simple polygon is less than π radians (180°), then the polygon is called convex. In contrast, an exterior angle (also called an or turning angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side.Weisstein, Eric W. "Exterior Angle Bisector." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ExteriorAngleBisector.htmlPosamentier, Alfred S., and Lehmann, Ingmar. ''The Secrets of Triangles'', Prometheus Books, 2012. Properties * The sum of the internal angle and the external angle on the same vertex is π radians (180°). * The sum of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible or evenly divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder. Definition An integer is divisible by a nonzero integer if there exists an integer such that n=km. This is written as :m\mid n. Other ways of saying the same thing are that divides , is a divisor of , is a factor of , and is a multiple of . If does not divide , then the notation is m\not\mid n. Usually, is required to be nonzero, but is allowed to be zero. With this convention, m \mid 0 for every nonzero integer . Some definitions omit the requirement that m be nonzero. General Divisors can be negative as well as positive, although sometimes the term is restricted to positive divisors. For example, there are six divisors of 4; they ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rational Number
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all rational numbers, also referred to as "the rationals", the field of rationals or the field of rational numbers is usually denoted by boldface , or blackboard bold \mathbb. A rational number is a real number. The real numbers that are rational are those whose decimal expansion either terminates after a finite number of digits (example: ), or eventually begins to repeat the same finite sequence of digits over and over (example: ). This statement is true not only in base 10, but also in every other integer base, such as the binary and hexadecimal ones (see ). A real number that is not rational is called irrational. Irrational numbers include , , , and . Since the set of rational numbers is countable, and the set of real numbers is uncountable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spirolateral 1-12-3432 60
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 gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spirolateral 2-3-4-90
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. 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 gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equiangular Pentagon2 60
Equiangular may refer to: *Equiangular lines, a set of lines where every pair of lines makes the same angle *Equiangular polygon, a polygon with equal angles *Logarithmic spiral or equiangular spiral, a type of geometric spiral *Unicode Unicode, formally The Unicode Standard,The formal version reference is is an information technology Technical standard, standard for the consistent character encoding, encoding, representation, and handling of Character (computing), text expre ... symbol represents the equiangular relation {{Disambiguation sv:Likvinklig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spirolateral 112-1-1-2 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. 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 gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crossed Rectangle
In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a ''square''. The term " oblong" is occasionally used to refer to a non-square rectangle. A rectangle with vertices ''ABCD'' would be denoted as . The word rectangle comes from the Latin ''rectangulus'', which is a combination of ''rectus'' (as an adjective, right, proper) and ''angulus'' (angle). A crossed rectangle is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals (therefore only two sides are parallel). It is a special case of an antiparallelogram, and its angles are not right angles and not all equal, though opposite angles are equal. Other geometries, such as spherical, elliptic, and hyperboli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spirolateral -1 2 60
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 gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unexpected Closed Spirolateral 7 90
Unexpected may refer to: Film and television * ''Unexpected'' (2005 film), an Italian documentary directed by Domenico Distilo * ''Unexpected'' (2015 film), an American film directed by Kris Swanberg * ''The Unexpected'' (TV series), a 1950s TV anthology series * "Unexpected" (''Heroes''), a television episode * "Unexpected" (''Star Trek: Enterprise''), a television episode Literature * ''The Unexpected'' (1968 comic book), a 1968–1982 DC Comics horror-fantasy series, a continuation of ''Tales of the Unexpected'' * ''The Unexpected'' (2018 comic book), a 2018–2019 DC Comics superhero series * ''The Unexpected'' (novel), a 2000 ''Animorphs'' novel by K.A. Applegate Music * ''Unexpected'' (Angie Stone album) or the title song, 2008 * ''Unexpected'' (Levina album), 2017 * ''Unexpected'' (Lumidee album), 2007 * ''Unexpected'' (Michelle Williams album) or the title song, 2008 * ''Unexpected'' (Sandy Mölling album) or the title song (see below), 2004 *''Unexpected'', an albu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
