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Constructible Polygons
Constructibility or constructability may refer to: * Constructability or construction feasibility review, a process in construction design whereby plans are reviewed by others familiar with construction techniques and materials to assess whether the design is actually buildable * Constructible strategy game, a tabletop strategy game employing pieces assembled from components Mathematics * Compass-and-straightedge construction * Constructible point, a point in the Euclidean plane that can be constructed with compass and straightedge * Constructible number, a complex number associated to a constructible point * Constructible polygon, a regular polygon that can be constructed with compass and straightedge * Constructible sheaf, a certain kind of sheaf of abelian groups * Constructible set (topology), a finite union of locally closed sets * Constructible topology In commutative algebra, the constructible topology on the spectrum \operatorname(A) of a commutative ring A is a topol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constructability
Constructability (or buildability) is a concept that denotes ease of construction. It can be central to project management techniques to review construction processes from start to finish during pre-construction phase. Buildability assessment is employed to identify obstacles before a project is actually built to reduce or prevent errors, delays, and cost overruns. CII defines constructibility as “the optimal use of construction knowledge and experience in planning, design, procurement, and field operations to achieve overall project objectives”. The term "constructability" can also define the ease and efficiency with which structures can be built. The more constructible a structure is, the more economical it will be. Constructability is in part a reflection of the quality of the design documents; that is, if the design documents are difficult to understand and interpret, the project will be difficult to build. The term refers to: * the extent to which the design of the buil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constructible Strategy Game
A constructible strategy game (CSG) (also spelled constructable strategy game) is a tabletop strategy game employing pieces assembled from components. WizKids was the first to label a game as a CSG when they released their game ''Pirates of the Spanish Main'' in 2004. Internally, the term was coined by then-WizKids Communications Director Jason Mical to describe the game where players assemble ships from hulls, masts, and deck pieces punched out of credit card-like plastic (polystyrene). A second CSG from WizKids, '' Rocketmen'', was released in summer 2005, and a NASCAR-themed CSG called '' Race Day'' came out later that year. Both ''Rocketmen'' and ''Race Day'' were later discontinued. WizKids now utilizes the term "PocketModel" to describe this genre, as with Star Wars PocketModel Trading Card Game and the modern Pirates of the Spanish Main website. White Wolf, Inc. released their own CSG, ''Racer Knights of Falconus'', under their Arthaus Publishing imprint in mid-2005. W ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compass-and-straightedge Construction
In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a pair of compasses. The idealized ruler, known as a straightedge, is assumed to be infinite in length, have only one edge, and no markings on it. The compass is assumed to have no maximum or minimum radius, and is assumed to "collapse" when lifted from the page, so may not be directly used to transfer distances. (This is an unimportant restriction since, using a multi-step procedure, a distance can be transferred even with a collapsing compass; see compass equivalence theorem. Note however that whilst a non-collapsing compass held against a straightedge might seem to be equivalent to marking it, the neusis construction is still impermissible and this is what unmarked really means: see Markable rulers below.) More formally, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constructible Point
In geometry and algebra, a real number r is constructible if and only if, given a line segment of unit length, a line segment of length , r, can be constructed with compass and straightedge in a finite number of steps. Equivalently, r is constructible if and only if there is a closed-form expression for r using only integers and the operations for addition, subtraction, multiplication, division, and square roots. The geometric definition of constructible numbers motivates a corresponding definition of constructible points, which can again be described either geometrically or algebraically. A point is constructible if it can be produced as one of the points of a compass and straight edge construction (an endpoint of a line segment or crossing point of two lines or circles), starting from a given unit length segment. Alternatively and equivalently, taking the two endpoints of the given segment to be the points (0, 0) and (1, 0) of a Cartesian coordinate system, a point is constr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constructible Number
In geometry and algebra, a real number r is constructible if and only if, given a line segment of unit length, a line segment of length , r, can be constructed with compass and straightedge in a finite number of steps. Equivalently, r is constructible if and only if there is a closed-form expression for r using only integers and the operations for addition, subtraction, multiplication, division, and square roots. The geometric definition of constructible numbers motivates a corresponding definition of constructible points, which can again be described either geometrically or algebraically. A point is constructible if it can be produced as one of the points of a compass and straight edge construction (an endpoint of a line segment or crossing point of two lines or circles), starting from a given unit length segment. Alternatively and equivalently, taking the two endpoints of the given segment to be the points (0, 0) and (1, 0) of a Cartesian coordinate system, a point is const ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constructible Polygon
In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon is not. There are infinitely many constructible polygons, but only 31 with an odd number of sides are known. Conditions for constructibility Some regular polygons are easy to construct with compass and straightedge; others are not. The ancient Greek mathematicians knew how to construct a regular polygon with 3, 4, or 5 sides, and they knew how to construct a regular polygon with double the number of sides of a given regular polygon.Bold, Benjamin. ''Famous Problems of Geometry and How to Solve Them'', Dover Publications, 1982 (orig. 1969). This led to the question being posed: is it possible to construct ''all'' regular polygons with compass and straightedge? If not, which ''n''-gons (that is, polygons with ''n'' edges) are constructible and which are not? Carl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constructible Sheaf
In mathematics, a constructible sheaf is a sheaf of abelian groups over some topological space ''X'', such that ''X'' is the union of a finite number of locally closed subsets on each of which the sheaf is a locally constant sheaf. It has its origins in algebraic geometry, where in étale cohomology constructible sheaves are defined in a similar way . For the derived category of constructible sheaves, see a section in ℓ-adic sheaf. The finiteness theorem in étale cohomology states that the higher direct images of a constructible sheaf are constructible. Definition of étale constructible sheaves on a scheme ''X'' Here we use the definition of constructible étale sheaves from the book by Freitag and Kiehl referenced below. In what follows in this subsection, all sheaves \mathcal on schemes X are étale sheaves unless otherwise noted. A sheaf \mathcal is called constructible if X can be written as a finite union of locally closed subschemes i_Y:Y \to X such that for each subsche ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constructible Set (topology)
In topology, constructible sets are a class of subsets of a topological space that have a relatively "simple" structure. They are used particularly in algebraic geometry and related fields. A key result known as ''Chevalley's theorem'' in algebraic geometry shows that the image of a constructible set is constructible for an important class of mappings (more specifically morphisms) of algebraic varieties (or more generally schemes). In addition, a large number of "local" geometric properties of schemes, morphisms and sheaves are (locally) constructible. Constructible sets also feature in the definition of various types of constructible sheaves in algebraic geometry and intersection cohomology. Definitions A simple definition, adequate in many situations, is that a constructible set is a finite union of locally closed sets. (A set is locally closed if it is the intersection of an open set and closed set.) However, a modification and another slightly weaker definition are needed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constructible Topology
In commutative algebra, the constructible topology on the spectrum \operatorname(A) of a commutative ring A is a topology where each closed set is the image of \operatorname (B) in \operatorname(A) for some algebra ''B'' over ''A''. An important feature of this construction is that the map \operatorname(B) \to \operatorname(A) is a closed map with respect to the constructible topology. With respect to this topology, \operatorname(A) is a compact, Hausdorff, and totally disconnected topological space (i.e., a Stone space). In general, the constructible topology is a finer topology than the Zariski topology, and the two topologies coincide if and only if A / \operatorname(A) is a von Neumann regular ring, where \operatorname(A) is the nilradical of ''A''. Despite the terminology being similar, the constructible topology is not the same as the set of all constructible sets. See also *Constructible set (topology) In topology, constructible sets are a class of subsets of a topologic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constructible Universe
In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted by , is a particular class of sets that can be described entirely in terms of simpler sets. is the union of the constructible hierarchy . It was introduced by Kurt Gödel in his 1938 paper "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis". In this paper, he proved that the constructible universe is an inner model of ZF set theory (that is, of Zermelo–Fraenkel set theory with the axiom of choice excluded), and also that the axiom of choice and the generalized continuum hypothesis are true in the constructible universe. This shows that both propositions are consistent with the basic axioms of set theory, if ZF itself is consistent. Since many other theorems only hold in systems in which one or both of the propositions is true, their consistency is an important result. What is can be thought of as being built in "stages" resembling the constr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constructible Function
In complexity theory, a time-constructible function is a function ''f'' from natural numbers to natural numbers with the property that ''f''(''n'') can be constructed from ''n'' by a Turing machine in the time of order ''f''(''n''). The purpose of such a definition is to exclude functions that do not provide an upper bound on the runtime of some Turing machine. Time-constructible definitions There are two different definitions of a time-constructible function. In the first definition, a function ''f'' is called time-constructible if there exists a positive integer ''n''0 and Turing machine ''M'' which, given a string 1''n'' consisting of ''n'' ones, stops after exactly ''f''(''n'') steps for all ''n'' ≥ ''n''0. In the second definition, a function ''f'' is called time-constructible if there exists a Turing machine ''M'' which, given a string 1''n'', outputs the binary representation of ''f''(''n'') in '' O''(''f''(''n'')) time (a unary representation may be used instead, since th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
