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The odd graph O_n of order n is a graph having vertices given by the (n-1)-subsets of {1,...,2n-1} such that two vertices are connected by an edge iff the associated subsets ...

An oriented graph is a directed graph having no symmetric pair of directed edges. A complete oriented graph is called a tournament. The numbers of oriented graphs on n=1, 2, ...

The orthocentroidal circle of a triangle DeltaABC is a central circle having the segment joining the triangle centroid G and orthocenter H of DeltaABC as its diameter ...

The orthopoles of a line l with respect to the four triangles formed by three out of four vertices of any quadrilateral ABCD lie on a straight line L known as the orthopolar ...

The prescription that a trigonometry identity can be converted to an analogous identity for hyperbolic functions by expanding, exchanging trigonometric functions with their ...

The outer Soddy center (or outer Soddy point) is the center of the outer Soddy circle. It is equivalent to the isoperimetric point X_(176) (Kimberling 1994) and has ...

The outer Soddy circle is the solution to the four coins problem. It has circle function l=((-a+b+c)^2[f(a,b,c)+16g(a,b,c)rs])/(4bc[(a^2+b^2+c^2)-2(ab+bc+ca)+8rs]^4), (1) ...

PEMDAS is an acronym used primarily in the United States as a mechanism to pedagogically enforce the order rules of computational precedence. PEMDAS is explained as follows: ...

The P versus NP problem is the determination of whether all NP-problems are actually P-problems. If P and NP are not equivalent, then the solution of NP-problems requires (in ...

Given any set B, the associated pair groupoid is the set B×B with the maps alpha(a,b)=a and beta(a,b)=b, and multiplication (a,b)·(b,c)=(a,c). The inverse is ...