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The dimension of an object is a topological measure of the size of its covering properties. Roughly speaking, it is the number of coordinates needed to specify a point on the ...

The curve produced by fixed point P on the circumference of a small circle of radius b rolling around the inside of a large circle of radius a>b. A hypocycloid is therefore a ...

An inner product is a generalization of the dot product. In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar. ...

A one-person game played on a rectangular lattice of lamps which can be turned on and off. A move consists of flipping a "switch" inside one of the squares, thereby toggling ...

The regular pentagon is the regular polygon with five sides, as illustrated above. A number of distance relationships between vertices of the regular pentagon can be derived ...

Two graphs which contain the same number of graph vertices connected in the same way are said to be isomorphic. Formally, two graphs G and H with graph vertices ...

The pathological function f_a(x)=sum_(k=1)^infty(sin(pik^ax))/(pik^a) (originally defined for a=2) that is continuous but differentiable only on a set of points of measure ...

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 ...

The sinc function sinc(x), also called the "sampling function," is a function that arises frequently in signal processing and the theory of Fourier transforms. The full name ...

Vassiliev invariants, discovered around 1989, provided a radically new way of looking at knots. The notion of finite type (a.k.a. Vassiliev) knot invariants was independently ...