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A positive measure is a measure which is a function from the measurable sets of a measure space to the nonnegative real numbers. Sometimes, this is what is meant by measure, ...

Any system of phi(n) integers, where phi(n) is the totient function, representing all the residue classes relatively prime to n is called a reduced residue system (Nagell ...

If f is analytic on a domain U, then a point z_0 on the boundary partialU is called regular if f extends to be an analytic function on an open set containing U and also the ...

A beautiful class of polyhedra composed of rhombic faces discovered accidentally by R. Towle while attempting to develop a function to create a rhombic hexahedron from a ...

The function giving the volume of the spherical quadrectangular tetrahedron: V=(pi^2)/8f(pi/p,pi/q,pi/r), (1) where (2) and D=sqrt(cos^2xcos^2z-cos^2y). (3)

The Schoute center is the inverse of the symmedian point in the circumcircle. It has triangle center function alpha_(187)=a(2a^2-b^2-c^2) and corresponds to Kimberling center ...

The first mid-arc point is the triangle center with triangle center function alpha_(178)=[cos(1/2B)+cos(1/2C)]csc(1/2A). It is Kimberling center X_(178).

The perspector of the first Morley triangle with reference triangle DeltaABC is called the second Morley center. Its triangle center function is alpha_(357)=sec(1/3A), which ...

The transformation T(x) = frac(1/x) (1) = 1/x-|_1/x_|, (2) where frac(x) is the fractional part of x and |_x_| is the floor function, that takes a continued fraction ...

Let f(x) be a nonnegative and monotonic decreasing function in [a,b] and g(x) such that 0<=g(x)<=1 in [a,b], then int_(b-k)^bf(x)dx<=int_a^bf(x)g(x)dx<=int_a^(a+k)f(x)dx, ...