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Is there a planar convex set having two distinct equichordal points? The problem was first proposed by Fujiwara (1916) and Blaschke et al. (1917), but long defied solution. ...

This problem is NP-complete (Garey and Johnson 1983).

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 ...

The grid shading problem is the problem of proving the unimodality of the sequence {a_1,a_2,...,a_(mn)}, where for fixed m and n, a_i is the number of partitions of i with at ...

In a given acute triangle DeltaABC, find the inscribed triangle whose perimeter is as small as possible. The answer is the orthic triangle of DeltaABC. The problem was ...

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 regions into which space can be divided by n mutually intersecting spheres is N=1/3n(n^2-3n+8), giving 2, 4, 8, 16, 30, 52, 84, ... (OEIS A046127) for n=1, 2, ...

The average number of regions N(n) into which n lines divide a square is N^_(n)=1/(16)n(n-1)pi+n+1 (Santaló 1976; Finch 2003, p. 481). The maximum number of sequences is ...

A boundary value problem is a problem, typically an ordinary differential equation or a partial differential equation, which has values assigned on the physical boundary of ...

The small world problem asks for the probability that two people picked at random have at least one acquaintance in common.