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A removable singularity is a singular point z_0 of a function f(z) for which it is possible to assign a complex number in such a way that f(z) becomes analytic. A more ...

A right trapezoid is a trapezoid having two right angles. As illustrated above, the area of a right trapezoid is A = ah_2-1/2(h_2-h_1)a (1) = 1/2a(h_1+h_2). (2) A right ...

If J is a simple closed curve in R^2, the closure of one of the components of R^2-J is homeomorphic with the unit 2-ball. This theorem may be proved using the Riemann mapping ...

A seminorm is a function on a vector space V, denoted ||v||, such that the following conditions hold for all v and w in V, and any scalar c. 1. ||v||>=0, 2. ||cv||=|c|||v||, ...

Separation of variables is a method of solving ordinary and partial differential equations. For an ordinary differential equation (dy)/(dx)=g(x)f(y), (1) where f(y)is nonzero ...

The angles S_1=A_1/2 and S_2=A_2/2 obtained from solving sin(x+omega)=2sinomega (1) for x=A_1,A_2, where omega is the Brocard angle. The half-angles A_1 and A_2 are given by ...

A relation < is a strict order on a set S if it is 1. Irreflexive: a<a does not hold for any a in S. 2. Asymmetric: if a<b, then b<a does not hold. 3. Transitive: a<b and b<c ...

A surface in 3-space can be parameterized by two variables (or coordinates) u and v such that x = x(u,v) (1) y = y(u,v) (2) z = z(u,v). (3) If a surface is parameterized as ...

A tetractys, also called a tetraktys or decad, is an arrangement of 10 points in the form of a triangle with 1 point in the first row, two in the second, three in the third, ...

A number of attractive 18-compounds of the regular tetrahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...