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The mean triangle area A^_ is the average area of a triangle in triangle picking within some given shape. As summarized in the following table, it is possible to compute the ...

An n-he (a term coined by Brendan Owen) is a shape formed from a polyhex by removing half of each hexagon in such a way that the remaining pieces are connected (Clarke). The ...

Consider a two-dimensional tessellation with q regular p-gons at each polygon vertex. In the plane, (1-2/p)pi=(2pi)/q (1) 1/p+1/q=1/2, (2) so (p-2)(q-2)=4 (3) (Ball and ...

An m-ary n-ic polynomial (i.e., a homogeneous polynomial with constant coefficients of degree n in m independent variables).

The sequence of binary digits of the Thue constant, 0.110110111110110111110110110..._2 (OEIS A014578). A recurrence plot of the limiting value of this sequence is illustrated ...

A necessary and sufficient condition for a curve to be a helix is that the ratio of curvature to torsion be constant.

The Balaban index J is a graph index defined for a graph on n nodes, m edges, and c connected components by J=m/(gamma+1)sum_((i,j) in E(G))(D_iD_j)^(-1/2), where gamma=m-n+c ...

The dual of Pascal's theorem (Casey 1888, p. 146). It states that, given a hexagon circumscribed on a conic section, the lines joining opposite polygon vertices (polygon ...

Let a tree S be a subgraph of a cubic graph G. The graph excision G circleminus S is the graph resulting from removing the tree, then merging the edges. For example, if in ...

The hexagram is the star polygon {6/2}, also known as the star of David or Solomon's seal, illustrated at left above. It appears as one of the clues in the novel The Da Vinci ...