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An integer which is expressible in more than one way in the form x^2+Dy^2 or x^2-Dy^2 where x^2 is relatively prime to Dy^2. If the integer is expressible in only one way, it ...

Due to Lebesgue and Brouwer. If an n-dimensional figure is covered in any way by sufficiently small subregions, then there will exist points which belong to at least n+1 of ...

In general, a frieze consists of repeated copies of a single motif. b ; a d; c Conway and Guy (1996) define a frieze pattern as an arrangement of numbers at the intersection ...

The problem of polygon intersection seeks to determine if two polygons intersect and, if so, possibly determine their intersection. For example, the intersection of the two ...

A circle packing is called rigid (or "stable") if every circle is fixed by its neighbors, i.e., no circle can be translated without disturbing other circles of the packing ...

Given a triangle with angles (pi/p, pi/q, pi/r), the resulting symmetry group is called a (p,q,r) triangle group (also known as a spherical tessellation). In three ...

A plane-filling arrangement of plane figures or its generalization to higher dimensions. Formally, a tiling is a collection of disjoint open sets, the closures of which cover ...

The study of efficient algorithms for solving geometric problems. Examples of problems treated by computational geometry include determination of the convex hull and Voronoi ...

Any partition of the plane into regions of equal area has perimeter at least that of the regular hexagonal grid (i.e., the honeycomb, illustrated above). Pappus refers to the ...

The café wall illusion, sometimes also called the Münsterberg illusion (Ashton Raggatt McDougall 2006), is an optical illusion produced by a black and white rectangular ...