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Externally erect a square on the side BC. Now join the new vertices S_(AB) and S_AC of this square with the vertex A, marking the points of intersection Q_(A,BC) and ...

The sum of the first n odd numbers is a square number, sum_(k=1)^n(2k-1)=n^2. A sort of converse also exists, namely the difference of the nth and (n-1)st square numbers is ...

Rényi's polynomial is the polynomial (Rényi 1947, Coppersmith and Davenport 1991) that has 29 terms and whose square has 28, making it a sparse polynomial square.

The granny knot is a composite knot of six crossings consisting of a knot sum of two left-handed trefoils with the same orientation (Rolfsen 1976, p. 220). The granny knot ...

The unique magic square of order three. The Lo Shu is an associative magic square, but not a panmagic square.

An array is a "list of lists" with the length of each level of list the same. The size (sometimes called the "shape") of a d-dimensional array is then indicated as ...

Find a way to stack a square of cannonballs laid out on the ground into a square pyramid (i.e., find a square number which is also square pyramidal). This corresponds to ...

A heterosquare is an n×n array of the integers from 1 to n^2 such that the rows, columns, and diagonals have different sums. (By contrast, in a magic square, they have the ...

An attractive tiling of the square composed of two types of triangular tiles. It consists of 16 equilateral triangles and 32 15 degrees-15 degrees-150 degrees isosceles ...

Tiling of a Möbius strip can be performed immediately by carrying over a tiling of a rectangle with the same two-sided surface area. However, additional tilings are possible ...