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Each curve in this example is a locus defined as the conchoid of the point P and the line l.In this example, P is 8 cm from l. In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.
The tiering of qualifications allows a subset of grades to be reached in a specific tier's paper. Formerly many subjects were tiered, but with the mid-2010s reform the number of tiered subjects reduced dramatically, including the removal of tiering from the GCSE English specifications. Untiered papers allow any grade to be achieved.
The ancient Greeks classified constructions into three major categories, depending on the complexity of the tools required for their solution. If a construction used only a straightedge and compass, it was called planar; if it also required one or more conic sections (other than the circle), then it was called solid; the third category included ...
Universal constructions are functorial in nature: if one can carry out the construction for every object in a category C then one obtains a functor on C. Furthermore, this functor is a right or left adjoint to the functor U used in the definition of the universal property. [2] Universal properties occur everywhere in mathematics.
Archimedes Geo3D is a shareware program designed for 3D geometric constructions. It extends traditional ruler and compass constructions into 3D space, allowing users to work with elements such as points, lines, circles, planes, spheres, vectors, and loci. This software is compatible with Windows, macOS, and Linux platforms.
The possible topologies on a fixed set X are partially ordered: a topology τ 1 is said to be coarser than another topology τ 2 (notation: τ 1 ⊆ τ 2) if every open subset with respect to τ 1 is also open with respect to τ 2. Then, the identity map. id X: (X, τ 2) → (X, τ 1) is continuous if and only if τ 1 ⊆ τ 2 (see also ...
In mathematics a stack or 2-sheaf is, roughly speaking, a sheaf that takes values in categories rather than sets. Stacks are used to formalise some of the main constructions of descent theory , and to construct fine moduli stacks when fine moduli spaces do not exist.
constructions that in addition to this use conic sections (ellipses, parabolas, hyperbolas); constructions that needed yet other means of construction, for example neuseis. In the end the use of neusis was deemed acceptable only when the two other, higher categories of constructions did not offer a solution.