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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 ...

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 ...

If a number fails Miller's primality test for some base a, it is not a prime. If the number passes, it may be a prime. A composite number passing Miller's test is called a ...

In French and German usage, one milliard equals 10^9=1000000000. American usage does not have a number called the milliard, instead using the term billion to denote 10^9. ...

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, ...

Mills' constant can be defined as the least theta such that f_n=|_theta^(3^n)_| is prime for all positive integers n (Caldwell and Cheng 2005). The first few f_n for n=1, 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 ...