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Every module over a ring R contains a so-called "zero element" which fulfils the properties suggested by its name with respect to addition, 0+0=0, and with respect to ...

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Multivariable Calculus

An n-dimensional vector, i.e., a vector (x_1, x_2, ..., x_n) with n components. In dimensions n greater than or equal to two, vectors are sometimes considered synonymous with ...

Compass and straightedge geometric constructions dating back to Euclid were capable of inscribing regular polygons of 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, ...

If a, b, c, and d are points in the extended complex plane C^*, their cross ratio, also called the cross-ratio (Courant and Robbins 1996, p. 172; Durell 1928, p. 73), ...

Three circles packed inside a triangle such that each is tangent to the other two and to two sides of the triangle are known as Malfatti circles. The Malfatti configuration ...

Given a set of n+1 control points P_0, P_1, ..., P_n, the corresponding Bézier curve (or Bernstein-Bézier curve) is given by C(t)=sum_(i=0)^nP_iB_(i,n)(t), where B_(i,n)(t) ...

Instead of picking two points from the interior of the cube, instead pick two points on different faces of the unit cube. In this case, the average distance between the ...

The term domain has (at least) three different meanings in mathematics. The term domain is most commonly used to describe the set of values D for which a function (map, ...