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For a right triangle with legs a and b and hypotenuse c, a^2+b^2=c^2. (1) Many different proofs exist for this most fundamental of all geometric theorems. The theorem can ...

A ring in the mathematical sense is a set S together with two binary operators + and * (commonly interpreted as addition and multiplication, respectively) satisfying the ...

The Rogers-Ramanujan continued fraction is a generalized continued fraction defined by R(q)=(q^(1/5))/(1+q/(1+(q^2)/(1+(q^3)/(1+...)))) (1) (Rogers 1894, Ramanujan 1957, ...

The number of ways of partitioning a set of n elements into m nonempty sets (i.e., m set blocks), also called a Stirling set number. For example, the set {1,2,3} can be ...

A transcendental number is a (possibly complex) number that is not the root of any integer polynomial, meaning that it is not an algebraic number of any degree. Every real ...

The Tutte 12-cage, also called the Benson graph (Exoo and Jajcay 2008), is the unique 12-cage graph, equivalent to the generalized hexagon GH(2,2) and alternately called the ...

The Wiener sum index WS is a graph index defined for a graph on n nodes by WS=1/2sum_(i=1)^nsum_(j=1)^n((d)_(ij))/((Omega)_(ij)), where (d)_(ij) is the graph distance matrix ...

Let G be a group, and let S subset= G be a set of group elements such that the identity element I not in S. The Cayley graph associated with (G,S) is then defined as the ...

A circle packing is an arrangement of circles inside a given boundary such that no two overlap and some (or all) of them are mutually tangent. The generalization to spheres ...

The cubical graph is the Platonic graph corresponding to the connectivity of the cube. It is isomorphic to the generalized Petersen graph GP(4,1), bipartite Kneser graph ...