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A group action G×X->X is called free if, for all x in X, gx=x implies g=I (i.e., only the identity element fixes any x). In other words, G×X->X is free if the map G×X->X×X ...

Gabriel's horn, also called Torricelli's trumpet, is the surface of revolution of the function y=1/x about the x-axis for x>=1. It is therefore given by parametric equations ...

The Gelfand transform x|->x^^ is defined as follows. If phi:B->C is linear and multiplicative in the senses phi(ax+by)=aphi(x)+bphi(y) and phi(xy)=phi(x)phi(y), where B is a ...

Let l(x) be an nth degree polynomial with zeros at x_1, ..., x_n. Then the fundamental Hermite interpolating polynomials of the first and second kinds are defined by ...

The Jacobian of the derivatives partialf/partialx_1, partialf/partialx_2, ..., partialf/partialx_n of a function f(x_1,x_2,...,x_n) with respect to x_1, x_2, ..., x_n is ...

A hexahedral graph is a polyhedral graph on six vertices. There are seven distinct hexahedral graphs (illustrated above) which, through duality, correspond to seven convex ...

The incentral triangle DeltaI_AI_BI_C is the Cevian triangle of a triangle DeltaABC with respect to its incenter I. It is therefore also the triangle whose vertices are ...

The inner Napoleon circle, a term coined here for the first time, is the circumcircle of the inner Napoleon triangle. It has center at the triangle centroid G (and is thus ...

The Ivanov-Ivanov-Faradjev graph is a distance-regular graph on 990 vertices (Brouwer et al. 1989, p. 369). It has intersection array {7,6,4,4,4,1,1,1;1,1,1,2,4,4,6,7} and is ...

Kelvin defined the Kelvin functions bei and ber according to ber_nu(x)+ibei_nu(x) = J_nu(xe^(3pii/4)) (1) = e^(nupii)J_nu(xe^(-pii/4)), (2) = e^(nupii/2)I_nu(xe^(pii/4)) (3) ...