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A transformation T (a.k.a., map, function) over a domain D takes the elements X in D to elements Y in T(D), where the range (a.k.a., image) of T is defined as ...

Consecutive number sequences are sequences constructed by concatenating numbers of a given type. Many of these sequences were considered by Smarandache and so are sometimes ...

An additive cellular automaton is a cellular automaton whose rule is compatible with an addition of states. Typically, this addition is derived from modular arithmetic. ...

The Costa surface is a complete minimal embedded surface of finite topology (i.e., it has no boundary and does not intersect itself). It has genus 1 with three punctures ...

The cycloid is the locus of a point on the rim of a circle of radius a rolling along a straight line. It was studied and named by Galileo in 1599. Galileo attempted to find ...

The floor function |_x_|, also called the greatest integer function or integer value (Spanier and Oldham 1987), gives the largest integer less than or equal to x. The name ...

A Hamiltonian graph, also called a Hamilton graph, is a graph possessing a Hamiltonian cycle. A graph that is not Hamiltonian is said to be nonhamiltonian. A Hamiltonian ...

Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), the Hilbert function of M is the map ...

There are a number of algebraic equations known as the icosahedral equation, all of which derive from the projective geometry of the icosahedron. Consider an icosahedron ...

The Mertens function is the summary function M(n)=sum_(k=1)^nmu(k), (1) where mu(n) is the Möbius function (Mertens 1897; Havil 2003, p. 208). The first few values are 1, 0, ...