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The number of different triangles which have integer side lengths and perimeter n is T(n) = P(n,3)-sum_(1<=j<=|_n/2_|)P(j,2) (1) = [(n^2)/(12)]-|_n/4_||_(n+2)/4_| (2) = ...

An integral embedding of a graph, not to be confused with an integral graph, is a graph drawn such that vertices are distinct points and all graph edges have integer lengths. ...

A general integral transform is defined by g(alpha)=int_a^bf(t)K(alpha,t)dt, where K(alpha,t) is called the integral kernel of the transform.

The computation of points or values between ones that are known or tabulated using the surrounding points or values. In particular, given a univariate function f=f(x), ...

An interpretation of first-order logic consists of a non-empty domain D and mappings for function and predicate symbols. Every n-place function symbol is mapped to a function ...

An interval is a connected portion of the real line. If the endpoints a and b are finite and are included, the interval is called closed and is denoted [a,b]. If the ...

A graph G=(V,E) is an interval graph if it captures the intersection relation for some set of intervals on the real line. Formally, P is an interval graph provided that one ...

Given a circle C with center O and radius k, then two points P and Q are inverse with respect to C if OP·OQ=k^2. If P describes a curve C_1, then Q describes a curve C_2 ...

The inverse erf function is the inverse function erf^(-1)(z) of the erf function erf(x) such that erf(erf^(-1)(x)) = x (1) erf^(-1)(erf(x)) = x, (2) with the first identity ...

Given a function f(x), its inverse f^(-1)(x) is defined by f(f^(-1)(x))=f^(-1)(f(x))=x. (1) Therefore, f(x) and f^(-1)(x) are reflections about the line y=x. In the Wolfram ...