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  2. Geometric algebra - Wikipedia

    en.wikipedia.org/wiki/Geometric_algebra

    In mathematics, a geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is built out of two fundamental operations, addition and the geometric product. Multiplication of vectors results in higher-dimensional objects called multivectors ...

  3. List of interactive geometry software - Wikipedia

    en.wikipedia.org/wiki/List_of_interactive...

    GeoGebra is software that combines geometry, algebra and calculus for mathematics education in schools and universities. It is available free of charge for non-commercial users. [6] License: open source under GPL license (free of charge) Languages: 55; Geometry: points, lines, all conic sections, vectors, parametric curves, locus lines

  4. GeoGebra - Wikipedia

    en.wikipedia.org/wiki/GeoGebra

    GeoGebra can store variables for numbers, vectors and points, calculate derivatives and integrals of functions, and has a full complement of commands like Root or Extremum. Teachers and students can use GeoGebra as an aid in formulating and proving geometric conjectures. GeoGebra's main features are: Interactive geometry environment (2D and 3D)

  5. Mathematical descriptions of the electromagnetic field

    en.wikipedia.org/wiki/Mathematical_descriptions...

    Elements and operations of the algebra can generally be associated with geometric meaning. The members of the algebra may be decomposed by grade (as in the formalism of differential forms) and the (geometric) product of a vector with a k-vector decomposes into a (k − 1)-vector and a (k + 1)-vector.

  6. Algebraic geometry and analytic geometry - Wikipedia

    en.wikipedia.org/wiki/Algebraic_geometry_and...

    In mathematics, algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals with complex manifolds and the more general analytic spaces defined locally by the vanishing of analytic functions of several complex variables. The deep relation between these ...

  7. Gauge theory gravity - Wikipedia

    en.wikipedia.org/wiki/Gauge_theory_gravity

    Gauge theory gravity (GTG) is a theory of gravitation cast in the mathematical language of geometric algebra. To those familiar with general relativity, it is highly reminiscent of the tetrad formalism although there are significant conceptual differences. Most notably, the background in GTG is flat, Minkowski spacetime.

  8. Plane-based geometric algebra - Wikipedia

    en.wikipedia.org/wiki/Plane-based_geometric_algebra

    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 ]

  9. List of algebraic geometry topics - Wikipedia

    en.wikipedia.org/wiki/List_of_algebraic_geometry...

    Quadric (algebraic geometry) Dimension of an algebraic variety; Hilbert's Nullstellensatz; Complete variety; Elimination theory; Gröbner basis; Projective variety; Quasiprojective variety; Canonical bundle; Complete intersection; Serre duality; Spaltenstein variety; Arithmetic genus, geometric genus, irregularity; Tangent space, Zariski ...

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