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  2. List of mathematical shapes - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_shapes

    Peak, an (n-3)-dimensional element For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak. Vertex figure : not itself an element of a polytope, but a diagram showing how the elements meet.

  3. Algebraic geometry - Wikipedia

    en.wikipedia.org/wiki/Algebraic_geometry

    The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like ...

  4. List of mathematical examples - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_examples

    This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of an isolated but particularly striking fact, as opposed to a proof of a ...

  5. 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 ...

  6. Real algebraic geometry - Wikipedia

    en.wikipedia.org/wiki/Real_algebraic_geometry

    Real algebra is the part of algebra which is relevant to real algebraic (and semialgebraic) geometry. It is mostly concerned with the study of ordered fields and ordered rings (in particular real closed fields ) and their applications to the study of positive polynomials and sums-of-squares of polynomials .

  7. Three-dimensional space - Wikipedia

    en.wikipedia.org/wiki/Three-dimensional_space

    A sphere in 3-space (also called a 2-sphere because it is a 2-dimensional object) consists of the set of all points in 3-space at a fixed distance r from a central point P. The solid enclosed by the sphere is called a ball (or, more precisely a 3-ball). The volume of the ball is given by

  8. Algebra - Wikipedia

    en.wikipedia.org/wiki/Algebra

    Algebra is the branch of mathematics that studies algebraic structures and the operations they use. [1] An algebraic structure is a non-empty set of mathematical objects, such as the integers, together with algebraic operations defined on that set, like addition and multiplication.

  9. Flat (geometry) - Wikipedia

    en.wikipedia.org/wiki/Flat_(geometry)

    For example, a line in two-dimensional space can be described by a single linear equation involving x and y: 3 x + 5 y = 8. {\displaystyle 3x+5y=8.} In three-dimensional space, a single linear equation involving x , y , and z defines a plane, while a pair of linear equations can be used to describe a line.

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