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The Haferman carpet is the beautiful fractal constructed using string rewriting beginning with a cell [1] and iterating the rules {0->[1 1 1; 1 1 1; 1 1 1],1->[0 1 0; 1 0 1; ...

For a nonzero real number r and a triangle DeltaABC, swing line segment BC about the vertex B towards vertex A through an angle rB. Call the line along the rotated segment L. ...

A point where a stable and an unstable separatrix (invariant manifold) from the same fixed point or same family intersect. Therefore, the limits lim_(k->infty)f^k(X) and ...

Given two topological spaces M and N, place an equivalence relationship on the continuous maps f:M->N using homotopies, and write f_1∼f_2 if f_1 is homotopic to f_2. Roughly ...

The illustrations above show a number of hyperbolic tilings, including the heptagonal once related to the Klein quartic. Escher was fond of depicting hyperbolic tilings, ...

An isoscelizer of an (interior) angle A in a triangle DeltaABC is a line through points I_(AB)I_(AC) where I_(AB) lies on AB and I_(AC) on AC such that DeltaAI_(AB)I_(AC) is ...

A matrix, also called a canonical box matrix, having zeros everywhere except along the diagonal and superdiagonal, with each element of the diagonal consisting of a single ...

The Jørgensen graph is a maximally linklessly embeddable graph on 8 vertices and 21 edges, where "maximal" means it is not a proper subgraph of another linklessly embeddable ...

Find the minimum number f(n) of subsets in a separating family for a set of n elements, where a separating family is a set of subsets in which each pair of adjacent elements ...

The problem of determining how many nonattacking kings can be placed on an n×n chessboard. For n=8, the solution is 16, as illustrated above (Madachy 1979). In general, the ...