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A Heronian tetrahedron, also called a perfect tetrahedron, is a (not necessarily regular) tetrahedron whose sides, face areas, and volume are all rational numbers. It ...

A hexahedron is a polyhedron with six faces. The figure above shows a number of named hexahedra, in particular the acute golden rhombohedron, cube, cuboid, hemicube, ...

The hyperbolic cosine is defined as coshz=1/2(e^z+e^(-z)). (1) The notation chx is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). This function describes the ...

The proof theories of propositional calculus and first-order logic are often referred to as classical logic. Intuitionistic propositional logic can be described as classical ...

Jacobi's imaginary transformations relate elliptic functions to other elliptic functions of the same type but having different arguments. In the case of the Jacobi elliptic ...

The m×n king graph is a graph with mn vertices in which each vertex represents a square in an m×n chessboard, and each edge corresponds to a legal move by a king. The number ...

Let z=re^(itheta)=x+iy be a complex number, then inequality |(zexp(sqrt(1-z^2)))/(1+sqrt(1-z^2))|<=1 (1) holds in the lens-shaped region illustrated above. Written explicitly ...

Let L=<L, v , ^ > and K=<K, v , ^ > be lattices, and let h:L->K. Then h is a lattice homomorphism if and only if for any a,b in L, h(a v b)=h(a) v h(b) and h(a ^ b)=h(a) ^ ...

If f(z) is analytic throughout the annular region between and on the concentric circles K_1 and K_2 centered at z=a and of radii r_1 and r_2<r_1 respectively, then there ...

The Lerch transcendent is generalization of the Hurwitz zeta function and polylogarithm function. Many sums of reciprocal powers can be expressed in terms of it. It is ...