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A Julia set with c=-0.390541-0.586788i. The fractal somewhat resembles the better known Mandelbrot set.

When can homology classes be realized as the image of fundamental classes of manifolds? The answer is known, and singular bordism groups provide insight into this problem.

Given a 111×111 (0,1)-matrix, fill 11 spaces in each row in such a way that all columns also have 11 spaces filled. Furthermore, each pair of rows must have exactly one ...

Sylvester's four-point problem asks for the probability q(R) that four points chosen at random in a planar region R have a convex hull which is a quadrilateral (Sylvester ...

Given three objects, each of which may be a point, line, or circle, draw a circle that is tangent to each. There are a total of ten cases. The two easiest involve three ...

The determination of whether a Turing machine will come to a halt given a particular input program. The halting problem is solvable for machines with less than four states. ...

If f(x,y) is an analytic function in a neighborhood of the point (x_0,y_0) (i.e., it can be expanded in a series of nonnegative integer powers of (x-x_0) and (y-y_0)), find a ...

The problem of determining the vertices of a Schwarz-Christoffel mapping (Krantz 1999, p. 176).

Brocard's problem asks to find the values of n for which n!+1 is a square number m^2, where n! is the factorial (Brocard 1876, 1885). The only known solutions are n=4, 5, and ...

The goat problem (or bull-tethering problem) considers a fenced circular field of radius a with a goat (or bull, or other animal) tied to a point on the interior or exterior ...