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The set of octonions, also sometimes called Cayley numbers and denoted O, consists of the elements in a Cayley algebra. A typical octonion is of the form ...

An oriented knot is an oriented link of one component, or equivalently, it is a knot which has been given an orientation. Given an oriented knot K, reversing the orientation ...

Let u and v be any functions of a set of variables (q_1,...,q_n,p_1,...,p_n). Then the expression ...

Given a subset S subset R^n and a real function f which is Gâteaux differentiable at a point x in S, f is said to be pseudoconvex at x if del f(x)·(y-x)>=0,y in ...

A quartic nonhamiltonian graph is a quartic graph that is nonhamiltonian. A number of such graphs are illustrated above. Van Cleemput and Zamfirescu (2018) gave a 39-vertex ...

The study of manifolds having a complete Riemannian metric. Riemannian geometry is a general space based on the line element ds=F(x^1,...,x^n;dx^1,...,dx^n), with F(x,y)>0 ...

The taxicab metric, also called the Manhattan distance, is the metric of the Euclidean plane defined by g((x_1,y_1),(x_2,y_2))=|x_1-x_2|+|y_1-y_2|, for all points ...

An attractive compound of three regular tetrahedra can be obtained by taking three tetrahedra with a C_2 axes aligned along the z-axis and rotating them a sixth of a turn ...

A number of attractive tetrahedron 6-compounds can be constructed. The first compound (left figures) is obtained by combining three stella octangula. A second can be obtained ...

The twinplex graph is the graph illustrated above in a number of embeddings which corresponds to the graph labeled Gamma_2 in Fischer and Little (2011). It is a cubic ...