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The Wiener sausage of radius a>0 is the random process defined by W^a(t)= union _(0<=s<=t)B_a(beta(s)) where here, beta(t) is the standard Brownian motion in R^d for t>=0 and ...

The regular icosahedron (often simply called "the" icosahedron) is the regular polyhedron and Platonic solid illustrated above having 12 polyhedron vertices, 30 polyhedron ...

A portion of a disk whose upper boundary is a (circular) arc and whose lower boundary is a chord making a central angle theta<pi radians (180 degrees), illustrated above as ...

Every bounded infinite set in R^n has an accumulation point. For n=1, an infinite subset of a closed bounded set S has an accumulation point in S. For instance, given a ...

The catacaustic of a cardioid for a radiant point along the x-axis is complicated function of x. For x=0 (i.e., with radiant point at the cusp), however, the catacaustic for ...

If g(x) is differentiable at the point x and f(x) is differentiable at the point g(x), then f degreesg is differentiable at x. Furthermore, let y=f(g(x)) and u=g(x), then ...

In 1989, P. Yff proved there is a unique configuration of isoscelizers for a given triangle such that all three have the same length and are concurrent (C. Kimberling, pers. ...

A connected graph is graph that is connected in the sense of a topological space, i.e., there is a path from any point to any other point in the graph. A graph that is not ...

The catacaustic of one arch of a cycloid given parametrically as x = t-sint (1) y = 1-cost (2) is a complicated expression for an arbitrary radiant point. For the case of the ...

A real function is said to be differentiable at a point if its derivative exists at that point. The notion of differentiability can also be extended to complex functions ...