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Plane-based geometric algebra is an application of Clifford algebra to modelling planes, lines, points, and rigid transformations. Generally this is with the goal of solving applied problems involving these elements and their intersections , projections , and their angle from one another in 3D space. [ 1 ]
Algebraic geometry codes, often abbreviated AG codes, are a type of linear code that generalize Reed–Solomon codes. The Russian mathematician V. D. Goppa constructed these codes for the first time in 1982.
7.1 Commutative algebra. 7.2 Sheaf theory. ... (projective geometry) Real projective plane; ... Algebraic geometry codes; Algebraic surfaces
In the late 1990s, plane-based geometric algebra and conformal geometric algebra (CGA) respectively provided a framework for euclidean geometry and classical geometries. [2] In practice, these and several derived operations allow a correspondence of elements, subspaces and operations of the algebra with geometric interpretations.
In projective geometry, duality or plane duality is a formalization of the striking symmetry of the roles played by points and lines in the definitions and theorems of projective planes. There are two approaches to the subject of duality, one through language ( § Principle of duality ) and the other a more functional approach through special ...
The Fano plane is an example of an (n 3)-configuration, that is, a set of n points and n lines with three points on each line and three lines through each point. The Fano plane, a (7 3)-configuration, is unique and is the smallest such configuration. [11]
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The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1 and is therefore a constructible number. In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length | | can be constructed with compass and straightedge in a finite number of steps.