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A sparse polynomial square is a square of a polynomial [P(x)]^2 that has fewer terms than the original polynomial P(x). Examples include Rényi's polynomial (1) (Rényi 1947, ...

Let H_n denote the nth hexagonal number and S_m the mth square number, then a number which is both hexagonal and square satisfies the equation H_n=S_m, or n(2n-1)=m^2. (1) ...

A number which is simultaneously octagonal and square. Let O_n denote the nth octagonal number and S_m the mth square number, then a number which is both octagonal and square ...

In a normal n×n Latin square, the entries in each row and column are chosen from a "global" set of n objects. Like a Latin square, a partial Latin square has no two rows or ...

The equilateral elongated square dipyramid, illustrated above together with its net, is Johnson solid J_(15). A version of the elongated square dipyramid that is "squashed" ...

Johnson solid J_(23).

A number which is simultaneously a pentagonal number P_n and a square number S_m. Such numbers exist when 1/2n(3n-1)=m^2. (1) Completing the square gives ...

Combine the two above squares on the left into the single large square on the right.

There are two types of squares inscribing reference triangle DeltaABC in the sense that all vertices lie on the sidelines of ABC. The first type has two adjacent vertices of ...

A centered polygonal number consisting of a central dot with four dots around it, and then additional dots in the gaps between adjacent dots. The general term is n^2+(n+1)^2, ...