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The distance d(u,v) between two vertices u and v of a finite graph is the minimum length of the paths connecting them (i.e., the length of a graph geodesic). If no such path ...

A group homomorphism is a map f:G->H between two groups such that the group operation is preserved:f(g_1g_2)=f(g_1)f(g_2) for all g_1,g_2 in G, where the product on the ...

The gyrobifastigium is an octahedron with on 8 vertices, 14 edges, and 8 faces. The equilateral gyrobifastigium is Johnson solid J_(26), consisting of two triangular prisms ...

A device consisting of two coupled pendula, usually oscillating at right angles to each other, which are attached to a pen. The resulting motion can produce beautiful, ...

Knuth's up-arrow notation is a notation invented by Knuth (1976) to represent large numbers in which evaluation proceeds from the right (Conway and Guy 1996, p. 60): m^n ...

An algebraic loop L is a Moufang loop if all triples of elements x, y, and z in L satisfy the Moufang identities, i.e., if 1. z(x(zy))=((zx)z)y, 2. x(z(yz))=((xz)y)z, 3. ...

What is the longest ladder that can be moved around a right-angled hallway of unit width? For a straight, rigid ladder, the answer is 2sqrt(2), which allows the ladder to ...

Let A be a normed (Banach) algebra. An algebraic left A-module X is said to be a normed (Banach) left A-module if X is a normed (Banach) space and the outer multiplication is ...

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 ...

A periodic minimal surface constructed by Schwarz using the following two principles: 1. If part of the boundary of a minimal surface is a straight line, then the reflection ...