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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 ...

Move a point Pi_0 along a line from an initial point to a final point. It traces out a line segment Pi_1. When Pi_1 is translated from an initial position to a final ...

The nth Ramanujan prime is the smallest number R_n such that pi(x)-pi(x/2)>=n for all x>=R_n, where pi(x) is the prime counting function. In other words, there are at least n ...

The symmedial triangle DeltaK_AK_BK_C (a term coined here for the first time), is the triangle whose vertices are the intersection points of the symmedians with the reference ...

Given a quadratic form Q(x,y)=x^2+y^2, (1) then Q(x,y)Q(x^',y^')=Q(xx^'-yy^',x^'y+xy^'), (2) since (x^2+y^2)(x^('2)+y^('2)) = (xx^'-yy^')^2+(xy^'+x^'y)^2 (3) = ...

Faà di Bruno's formula gives an explicit equation for the nth derivative of the composition f(g(t)). If f(t) and g(t) are functions for which all necessary derivatives are ...

For some constant alpha_0, alpha(f,z)<alpha_0 implies that z is an approximate zero of f, where alpha(f,z)=(|f(z)|)/(|f^'(z)|)sup_(k>1)|(f^((k))(z))/(k!f^'(z))|^(1/(k-1)). ...

An amicable quadruple as a quadruple (a,b,c,d) such that sigma(a)=sigma(b)=sigma(c)=sigma(d)=a+b+c+d, (1) where sigma(n) is the divisor function. If (a,b) and (x,y) are ...

An Appell sequence is a Sheffer sequence for (g(t),t). Roman (1984, pp. 86-106) summarizes properties of Appell sequences and gives a number of specific examples. The ...

Given a principal bundle pi:A->M, with fiber a Lie group G and base manifold M, and a group representation of G, say phi:G×V->V, then the associated vector bundle is ...