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While an equality A=B states that two mathematical expressions are equal, an inequation A!=B states that two expressions are not equal.

By the duality principle, for every polyhedron, there exists another polyhedron in which faces and polyhedron vertices occupy complementary locations. This polyhedron is ...

The constant e is base of the natural logarithm. e is sometimes known as Napier's constant, although its symbol (e) honors Euler. e is the unique number with the property ...

Extend Hilbert's inequality by letting p,q>1 and 1/p+1/q>=1, (1) so that 0<lambda=2-1/p-1/q<=1. (2) Levin (1937) and Stečkin (1949) showed that (3) and ...

If p>1, then Minkowski's integral inequality states that Similarly, if p>1 and a_k, b_k>0, then Minkowski's sum inequality states that [sum_(k=1)^n|a_k+b_k|^p]^(1/p) ...

In functional analysis, the term "Poincaré-Friedrichs inequality" is a term used to describe inequalities which are qualitatively similar to the classical Poincaré Inequality ...

Consider the sum (1) where the x_js are nonnegative and the denominators are positive. Shapiro (1954) asked if f_n(x_1,x_2,...,x_n)>=1/2n (2) for all n. It turns out ...

If P is a pedal point inside a triangle DeltaABC, and P_A, P_B, and P_C are the feet of the perpendiculars from P upon the respective sides BC, CA, and AB, then ...

The Gini coefficient (or Gini ratio) G is a summary statistic of the Lorenz curve and a measure of inequality in a population. The Gini coefficient is most easily calculated ...

There are a number of attractive polyhedron compounds consisting of two octahedra. The first (left figure) consists of two octahedra rotated above a common C_3 symmetry axes. ...