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Let j, r, and s be distinct integers (mod n), and let W_i be the point of intersection of the side or diagonal V_iV_(i+j) of the n-gon P=[V_1,...,V_n] with the transversal ...

A transformation in which all points along a given line L remain fixed while other points are shifted parallel to L by a distance proportional to their perpendicular distance ...

Given n mutually exclusive events A_1, ..., A_n whose probabilities sum to unity, then P(B)=P(B|A_1)P(A_1)+...+P(B|A_n)P(A_n), where B is an arbitrary event, and P(B|A_i) is ...

If the top and bottom bases of a solid are equal in area, lie in parallel planes, and every section of the solid parallel to the bases is equal in area to that of the base, ...

Let f be a family of meromorphic functions on the unit disk D which are not normal at 0. Then there exist sequences f_n in F, z_n, rho_n, and a nonconstant function f ...

A p-system of a set S is a sequence of subsets A_1, A_2, ..., A_p of S, among which some may be empty or coinciding with each other.

An important and fundamental axiom in set theory sometimes called Zermelo's axiom of choice. It was formulated by Zermelo in 1904 and states that, given any set of mutually ...

Any real function u(x,y) with continuous second partial derivatives which satisfies Laplace's equation, del ^2u(x,y)=0, (1) is called a harmonic function. Harmonic functions ...

A transformation of the form w=f(z)=(az+b)/(cz+d), (1) where a, b, c, d in C and ad-bc!=0, (2) is a conformal mapping called a linear fractional transformation. The ...

Reciprocation is an incidence-preserving transformation in which points are transformed into their polars. A projective geometry-like duality principle holds for ...