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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.
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.
Additional Mathematics is a qualification in mathematics, commonly taken by students in high-school (or GCSE exam takers in the United Kingdom). It features a range of problems set out in a different format and wider content to the standard Mathematics at the same level.
Using a markable ruler, regular polygons with solid constructions, like the heptagon, are constructible; and John H. Conway and Richard K. Guy give constructions for several of them. [20] The neusis construction is more powerful than a conic drawing tool, as one can construct complex numbers that do not have solid constructions.
In mathematics, general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology , geometric topology , and algebraic topology .
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.
In modern mathematics, they are generally defined as elements of a set called space, which is itself axiomatically defined. With these modern definitions, every geometric shape is defined as a set of points; this is not the case in synthetic geometry, where a line is another fundamental object that is not viewed as the set of the points through ...
In mathematics, the Mohr–Mascheroni theorem states that any geometric construction that can be performed by a compass and straightedge can be performed by a compass alone. It must be understood that "any geometric construction" refers to figures that contain no straight lines, as it is clearly impossible to draw a straight line without a ...
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