Search Results for ""

Let O and I be the circumcenter and incenter of a triangle with circumradius R and inradius r. Let d be the distance between O and I. Then d^2=R(R-2r) (Mackay 1886-1887; ...

The resolution principle, due to Robinson (1965), is a method of theorem proving that proceeds by constructing refutation proofs, i.e., proofs by contradiction. This method ...

A number of strongly regular graphs of several types derived from combinatorial design were identified by Goethals and Seidel (1970). Theorem 2.4 of Goethals and Seidel ...

The orthogonal decomposition of a vector y in R^n is the sum of a vector in a subspace W of R^n and a vector in the orthogonal complement W^_|_ to W. The orthogonal ...

A semialgebraic set is a subset of R^n which is a finite Boolean combination of sets of the form {x^_=(x_1,...,x_n):f(x^_)>0} and {x^_:g(x^_)=0}, where f and g are ...

The Banach density of a set A of integers is defined as lim_(d->infty)max_(n)(|{A intersection [n+1,...,n+d]}|)/d, if the limit exists. If the lim is replaced with lim sup or ...

Bertrand's postulate, also called the Bertrand-Chebyshev theorem or Chebyshev's theorem, states that if n>3, there is always at least one prime p between n and 2n-2. ...

Four or more points P_1, P_2, P_3, P_4, ... which lie on a circle C are said to be concyclic. Three points are trivially concyclic since three noncollinear points determine a ...

The Lyapunov condition, sometimes known as Lyapunov's central limit theorem, states that if the (2+epsilon)th moment (with epsilon>0) exists for a statistical distribution of ...

The Wolstenholme numbers are defined as the numerators of the generalized harmonic number H_(n,2) appearing in Wolstenholme's theorem. The first few are 1, 5, 49, 205, 5269, ...