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The (not necessarily regular) tetrahedron of least volume circumscribed around a convex body B with volume V is not known. If B is a parallelepiped, then the smallest-volume ...

The network flow problem considers a graph G with a set of sources S and sinks T and for which each edge has an assigned capacity (weight), and then asks to find the maximum ...

Determination of whether predicate P(x_1,...,x_n) is true or false for any given values of x_1, ..., x_n is called its decision problem. The decision problem for predicate ...

The P versus NP problem is the determination of whether all NP-problems are actually P-problems. If P and NP are not equivalent, then the solution of NP-problems requires (in ...

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. ...

Any partition of the plane into regions of equal area has perimeter at least that of the regular hexagonal grid (i.e., the honeycomb, illustrated above). Pappus refers to the ...

Find the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip (without friction) from one point to another in the least time. The term ...

As a consequence of Matiyasevich's refutation of Hilbert's 10th problem, it can be proved that there does not exist a general algorithm for solving a general quartic ...

An aperiodic monotile, also somewhat humorously known as an einstein (where "einstein" means "one stone", perhaps generalizable to "one tile," in German), is a single tile ...

The Earth-Moon problem is a special case of the empire problem for countries with m=2 disjoint regions, with one region of each country lying on the Earth and one on the Moon ...