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It is possible to find six points in the plane, no three on a line and no four on a circle (i.e., none of which are collinear or concyclic), such that all the mutual ...

A row-convex polyomino is a self-avoiding convex polyomino such that the intersection of any horizontal line with the polyomino has at most two connected components. A ...

In n dimensions for n>=5 the arrangement of hyperspheres whose convex hull has minimal content is always a "sausage" (a set of hyperspheres arranged with centers along a ...

The above two figures are rearrangements of each other, with the corresponding triangles and polyominoes having the same areas. Nevertheless, the bottom figure has an area ...

The Tusi couple is a 2-cusped hypocycloid obtained by rolling a circle of radius a inside a circle of radius 2a. The result is a line segment (Steinhaus 1999, p. 145; Kanas ...

The Wiener sausage of radius a>0 is the random process defined by W^a(t)= union _(0<=s<=t)B_a(beta(s)) where here, beta(t) is the standard Brownian motion in R^d for t>=0 and ...

The network flow problem considers a graph G with a set of sources S and sinks T and for which each edge has an assigned capacity (weight), and then asks to find the maximum ...

In general, the word "complement" refers to that subset F^' of some set S which excludes a given subset F. Taking F and its complement F^' together then gives the whole of ...

A pseudoforest is an undirected graph in which every connected component contains at most one graph cycle. A pseudotree is therefore a connected pseudoforest and a forest ...

A cylindrical projection of points on a unit sphere centered at O consists of extending the line OS for each point S until it intersects a cylinder tangent to the sphere at ...