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The Georges graph, illustrated above, is 50-node graph which is the smallest currently known example of a 3-connected bicubic nonhamiltonian graph. It is implemented in the ...

Successive points dividing a golden rectangle into squares lie on a logarithmic spiral (Wells 1991, p. 39; Livio 2002, p. 119) which is sometimes known as the golden spiral. ...

Let {a_n} be a nonnegative sequence and f(x) a nonnegative integrable function. Define A_n=sum_(k=1)^na_k (1) and F(x)=int_0^xf(t)dt (2) and take p>1. For sums, ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_7=f(x_7). Then Hardy's rule approximating the ...

The Heath-Brown-Moroz constant is defined by C_(Heath-Brown-Moroz) = product_(p)(1-1/p)^7(1+(7p+1)/(p^2)) (1) = 0.00131764115... (2) (OEIS A118228), where the product is ...

Let H be a heptagon with seven vertices given in cyclic order inscribed in a conic. Then the Pascal lines of the seven hexagons obtained by omitting each vertex of H in turn ...

A flexagon made by folding a strip into adjacent equilateral triangles. The number of states possible in a hexaflexagon is the Catalan number C_5=42.

A polyiamond composed of six equilateral triangles. The 12 hexiamonds are illustrated above. They are given the names bar, crook, crown, sphinx, snake, yacht, chevron, ...

The 21 assumptions which underlie the geometry published in Hilbert's classic text Grundlagen der Geometrie. The eight incidence axioms concern collinearity and intersection ...

A hyperbolic version of the Euclidean tetrahedron.