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A number taken to the power 2 is said to be squared, so x^2 is called "x squared." This terminology derives from the fact that the area of a square of edge length x is given ...

The Bernoulli inequality states (1+x)^n>1+nx, (1) where x>-1!=0 is a real number and n>1 an integer. This inequality can be proven by taking a Maclaurin series of (1+x)^n, ...

The exponential transform is the transformation of a sequence a_1, a_2, ... into a sequence b_1, b_2, ... according to the equation ...

A two-coloring of a complete graph K_n of n nodes which contains exactly the number of monochromatic forced triangles and no more (i.e., a minimum of R+B where R and B are ...

The word multiplicity is a general term meaning "the number of values for which a given condition holds." For example, the term is used to refer to the value of the totient ...

The word "order" is used in a number of different ways in mathematics. Most commonly, it refers to the number of elements in (e.g., conjugacy class order, graph order, group ...

There are a number of algebraic identities involving sets of four vectors. An identity known as Lagrange's identity is given by (AxB)·(CxD)=(A·C)(B·D)-(A·D)(B·C) (1) ...

Define a carefree couple as a pair of positive integers (a,b) such that a and b are relatively prime (i.e., GCD(a,b)=1) and a is squarefree. Similarly, define a strongly ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

The word "convergent" has a number of different meanings in mathematics. Most commonly, it is an adjective used to describe a convergent sequence or convergent series, where ...