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Given a set S of n nonnegative integers, the number partitioning problem requires the division of S into two subsets such that the sums of number in each subset are as close ...

Isolated resonances in a dynamical system can cause considerable distortion of preserved tori in their neighborhood, but they do not introduce any chaos into a system. ...

The root separation (or zero separation) of a polynomial P(x) with roots r_1, r_2, ... is defined by Delta(P)=min_(i!=j)|r_i-r_j|. There are lower bounds on how close two ...

In n dimensions for n>=5 the arrangement of hyperspheres whose convex hull has minimal content is always a "sausage" (a set of hyperspheres arranged with centers along a ...

Find the surface enclosing the maximum volume per unit surface area, I=V/S. The solution is a sphere, which has I_(sphere)=(4/3pir^3)/(4pir^2)=1/3r. The fact that a sphere ...

The number of equivalent hyperspheres in n dimensions which can touch an equivalent hypersphere without any intersections, also sometimes called the Newton number, contact ...

The map which takes points on the surface of a sphere S^2 to their antipodal points.

A cylindrical projection of points on a unit sphere centered at O consists of extending the line OS for each point S until it intersects a cylinder tangent to the sphere at ...

The diameter of a circle is the distance from a point on the circle to a point pi radians away, and is the maximum distance from one point on a circle to another. The ...

The problem of deciding if four colors are sufficient to color any map on a plane or sphere.