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The nearest integer function, also called nint or the round function, is defined such that nint(x) is the integer closest to x. While the notation |_x] is sometimes used to ...

A set is a finite or infinite collection of objects in which order has no significance, and multiplicity is generally also ignored (unlike a list or multiset). Members of a ...

A polyhedral graph is completely regular if the dual graph is also regular. There are only five types. Let rho be the number of graph edges at each node, rho^* the number of ...

The global clustering coefficient C of a graph G is the ratio of the number of closed trails of length 3 to the number of paths of length two in G. Let A be the adjacency ...

Consider a game where everyone in a classroom picks a number between 0 and 100. The person closest to half the average wins. Obviously, picking a number over 50 would be ...

Relationships between the number of singularities of plane algebraic curves. Given a plane curve, m = n(n-1)-2delta-3kappa (1) n = m(m-1)-2tau-3iota (2) iota = ...

The greatest common divisor, sometimes also called the highest common divisor (Hardy and Wright 1979, p. 20), of two positive integers a and b is the largest divisor common ...

A right triangle is triangle with an angle of 90 degrees (pi/2 radians). The sides a, b, and c of such a triangle satisfy the Pythagorean theorem a^2+b^2=c^2, (1) where the ...

N_phi(m) is the number of integers n for which the totient function phi(n)=m, also called the multiplicity of m (Guy 1994). Erdős (1958) proved that if a multiplicity occurs ...

The ring of fractions of an integral domain. The field of fractions of the ring of integers Z is the rational field Q, and the field of fractions of the polynomial ring ...