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Midpoint augmentation, a term introduced here, is a variant of conventional augmentation in which each facial polygon is replaced by a triangular polygon joining vertices ...

The radius rho of the midsphere of a polyhedron, also called the interradius. Let P be a point on the original polyhedron and P^' the corresponding point P on the dual. Then ...

Is it possible to cover completely the surface of a sphere with congruent, nonoverlapping arcs of great circles? Conway and Croft (1964) proved that it can be covered with ...

An inequality which implies the correctness of the Robertson conjecture (Milin 1964). de Branges (1985) proved this conjecture, which led to the proof of the full Bieberbach ...

A map projection given by the following transformation, x = lambda-lambda_0 (1) y = 5/4ln[tan(1/4pi+2/5phi)] (2) = 5/4sinh^(-1)[tan(4/5phi)]. (3) Here, x and y are the plane ...

Several cylindrical equidistant projections were devised by R. Miller. Miller's projections have standard parallels of phi_1=37 degrees30^' (giving minimal overall scale ...

det(i+j+mu; 2i-j)_(i,j=0)^(n-1)=2^(-n)product_(k=0)^(n-1)Delta_(2k)(2mu), where mu is an indeterminate, Delta_0(mu)=2, ...

The Mills ratio is defined as m(x) = 1/(h(x)) (1) = (S(x))/(P(x)) (2) = (1-D(x))/(P(x)), (3) where h(x) is the hazard function, S(x) is the survival function, P(x) is the ...

Let X be a locally convex topological vector space and let K be a compact subset of X. In functional analysis, Milman's theorem is a result which says that if the closed ...

A predictor-corrector method for solution of ordinary differential equations. The third-order equations for predictor and corrector are y_(n+1) = ...