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The amazing identity for all theta, where Gamma(z) is the gamma function. Equating coefficients of theta^0, theta^4, and theta^8 gives some amazing identities for the ...

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, ...