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If the knot K is the boundary K=f(S^1) of a singular disk f:D->S^3 which has the property that each self-intersecting component is an arc A subset f(D^2) for which f^(-1)(A) ...

The problem of finding the connection between a continuous function f on the boundary partialR of a region R with a harmonic function taking on the value f on partialR. In ...

The Heilbronn triangle problem is to place n>=3 points in a disk (square, equilateral triangle, etc.) of unit area so as to maximize the area Delta(n) of the smallest of the ...

Continuum percolation can be thought of as a continuous, uncountable version of percolation theory-a theory which, in its most studied form, takes place on a discrete, ...

A circular sector is a wedge obtained by taking a portion of a disk with central angle theta<pi radians (180 degrees), illustrated above as the shaded region. A sector with ...

The subset C of the Euclidean plane formed by the union of the x-axis, the line segment with interval [0,1] of the y-axis, and the sequence of segments with endpoints (1/n,0) ...

The geodesics in a complete Riemannian metric go on indefinitely, i.e., each geodesic is isometric to the real line. For example, Euclidean space is complete, but the open ...

The mean triangle area A^_ is the average area of a triangle in triangle picking within some given shape. As summarized in the following table, it is possible to compute the ...

Let two disks of radius r intersect one another perpendicularly and have a diameter in common. If the distance between the centers of the disks is sqrt(2) times their radius, ...

A knot K in S^3=partialD^4 is a slice knot if it bounds a disk Delta^2 in D^4 which has a tubular neighborhood Delta^2×D^2 whose intersection with S^3 is a tubular ...