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An integer-relation algorithm which is based on a partial sum of squares approach, from which the algorithm takes its name.

A pandiagonal perfect magic cube is a perfect magic cube that remains perfect when any single orthogonal section is "restacked" cyclically so that the ordering of any set of ...

A pandiagonal semiperfect magic cube is a semiperfect magic cube that remains semiperfect when any single orthogonal section is "restacked" cyclically so that the ordering of ...

A plane figure or solid compound consisting of multiple connected copies of a given base shape. For example, affixing n equal squares gives an n-polyomino, while affixing n ...

A polyomino-like object made by attaching squares joined either at sides or corners. Because neighboring squares can be in relation to one another as kings may move on a ...

Pythagoras's theorem states that the diagonal d of a square with sides of integral length s cannot be rational. Assume d/s is rational and equal to p/q where p and q are ...

Gardner showed how to dissect a square into eight and nine acute scalene triangles. W. Gosper discovered a dissection of a unit square into 10 acute isosceles triangles, ...

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 ...

As shown by Schnirelman (1944), a square can be inscribed in any closed convex curve, although it is not known if this holds true for every Jordan curve (Steinhaus 1999, p. ...

A stadium, also called a discorectangle, obround, or sausage body, is a geometric figure consisting of a rectangle with top and bottom lengths a whose ends are capped off ...