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Schmidt (1993) proposed the problem of determining if for any integer r>=2, the sequence of numbers {c_k^((r))}_(k=1)^infty defined by the binomial sums sum_(k=0)^n(n; ...

De Grey (2018) found the first examples of unit-distance graphs with chromatic number 5, thus demonstrating that the solution to the Hadwiger-Nelson problem (i.e., the ...

Given a ship with a known constant direction and speed v, what course should be taken by a chase ship in pursuit (traveling at speed V) in order to intercept the other ship ...

If r is the inradius of a circle inscribed in a right triangle with sides a and b and hypotenuse c, then r=1/2(a+b-c). (1) A Sangaku problem dated 1803 from the Gumma ...

The number 2^(1/3)=RadicalBox[2, 3] (the cube root of 2) which is to be constructed in the cube duplication problem. This number is not a Euclidean number although it is an ...

Given any assignment of n-element sets to the n^2 locations of a square n×n array, is it always possible to find a partial Latin square? The fact that such a partial Latin ...

Define the packing density eta of a packing of spheres to be the fraction of a volume filled by the spheres. In three dimensions, there are three periodic packings for ...

Angle trisection is the division of an arbitrary angle into three equal angles. It was one of the three geometric problems of antiquity for which solutions using only compass ...

The conjecture made by Belgian mathematician Eugène Charles Catalan in 1844 that 8 and 9 (2^3 and 3^2) are the only consecutive powers (excluding 0 and 1). In other words, ...

The Ramsey number R(m,n) gives the solution to the party problem, which asks the minimum number of guests R(m,n) that must be invited so that at least m will know each other ...