In mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object with certain properties by creating or providing a method for creating such an object. This is in contrast to a non-constructive proof (also known as an existence proof or pure existence theorem) which proves the validity of a proposition without considering an example.
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Constructive solid geometry
Constructive solid geometry (CSG) is a technique used in solid modeling. Constructive solid geometry allows a modeler to create a complex surface or object by using Boolean operators to combine objects. Often CSG presents a model or surface that appears visually complex, but is actually little more than cleverly combined or decombined objects. In 3D computer graphics and CAD CSG is often used in procedural modeling.
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CW complex
In topology, a CW complex is a type of topological space introduced by J. H. C. Whitehead to meet the needs of homotopy theory. This class of spaces is broader and has some better categorical properties than simplicial complexes, but still retains a combinatorial nature that allows for computation.
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Parametric equation
the butterfly curve. ]] In mathematics, parametric equation is a method of defining a relation using parameters. A simple kinematic example is when one uses a time parameter to determine the position, velocity, and other information about a body in motion. Abstractly, a parametric equation defines a relation as a set of equations. Therefore, it is somewhat more accurately defined as a parametric representation. It is part of regular parametric representation.
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Topology
Topology (from the Greek ¿¿¿¿¿, ¿place¿, and ¿¿¿¿¿, ¿study¿) is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing. It emerged through the development of concepts from geometry and set theory, such as space, dimension, and transformation. Ideas that are now classified as topological were expressed as early as 1736.
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Coordinate system
In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element on a manifold such as Euclidean space. The order of the coordinates is significant and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in 'the x-coordinate'.
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Euclidean space
In mathematics, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry, as well as the generalizations of these notions to higher dimensions. The term ¿Euclidean¿ distinguishes these spaces from the curved spaces of non-Euclidean geometry and Einstein's general theory of relativity, and is named for the Greek mathematician Euclid of Alexandria.
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Parametric family
In mathematics and its applications, a parametric family or a parameterized family is a family of objects whose definitions depend on a set of parameters. Common examples are parametrized (families of) functions, probability distributions, curves, shapes, etc..
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