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The term "arbelos" means shoemaker's knife in Greek, and this term is applied to the shaded area in the above figure which resembles the blade of a knife used by ancient ...

A Borel set is an element of a Borel sigma-algebra. Roughly speaking, Borel sets are the sets that can be constructed from open or closed sets by repeatedly taking countable ...

A set S in a metric space (S,d) is bounded if it has a finite generalized diameter, i.e., there is an R<infty such that d(x,y)<=R for all x,y in S. A set in R^n is bounded ...

A subset S of a topological space X is compact if for every open cover of S there exists a finite subcover of S.

A connected set is a set that cannot be partitioned into two nonempty subsets which are open in the relative topology induced on the set. Equivalently, it is a set which ...

The generalized diameter is the greatest distance between any two points on the boundary of a closed figure. The diameter of a subset E of a Euclidean space R^n is therefore ...

A set S and a binary operator * are said to exhibit closure if applying the binary operator to two elements S returns a value which is itself a member of S. The closure of a ...

The Tschirnhausen cubic is a plane curve given by the polar equation r=asec^3(1/3theta). (1) Letting theta=3tan^(-1)t gives the parametric equations x = a(1-3t^2) (2) y = ...

Let A be the area of a simply closed lattice polygon. Let B denote the number of lattice points on the polygon edges and I the number of points in the interior of the ...

Applying the stellation process to the icosahedron gives 20+30+60+20+60+120+12+30+60+60 cells of 11 different shapes and sizes (including the icosahedron itself). The ...