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An operator defined on a set S which takes two elements from S as inputs and returns a single element of S. Binary operators are called compositions by Rosenfeld (1968). Sets ...

The order-n bouquet graph B_n is a pseudograph consisting of a single vertex with n self-loops. The bouquet graph B_1 is a pseudograph that can be considered to correspond to ...

Gray (1997) defines Bour's minimal curve over complex z by x^' = (z^(m-1))/(m-1)-(z^(m+1))/(m+1) (1) y^' = i((z^(m-1))/(m-1)+(z^(m+1))/(m+1)) (2) z^' = (2z^m)/m, (3) and then ...

An n-bridge knot is a knot with bridge number n. The set of 2-bridge knots is identical to the set of rational knots. If L is a 2-bridge knot, then the BLM/Ho polynomial Q ...

The rank of a vector bundle is the dimension of its fiber. Equivalently, it is the maximum number of linearly independent local bundle sections in a trivialization. ...

A minimal surface given by the parametric equations x(u,v) = u-sinucoshv (1) y(u,v) = 1-cosucoshv (2) z(u,v) = 4sin(1/2u)sinh(1/2v) (3) (Gray 1997), or x(r,phi) = ...

The parameters alpha, beta, gamma, and delta which, like the three Euler angles, provide a way to uniquely characterize the orientation of a solid body. These parameters ...

The Christmas stocking theorem, also known as the hockey stick theorem, states that the sum of a diagonal string of numbers in Pascal's triangle starting at the nth entry ...

A concordant form is an integer triple (a,b,N) where {a^2+b^2=c^2; a^2+Nb^2=d^2, (1) with c and d integers. Examples include {14663^2+111384^2=112345^2; ...

A planar polygon is convex if it contains all the line segments connecting any pair of its points. Thus, for example, a regular pentagon is convex (left figure), while an ...