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The 4-polyhex illustrated above.

A pivot point of a curve is a fixed point Q such that points P lying on the curve and their (isogonal, isotomic, etc.) conjugates are collinear with Q.

The element in the diagonal of a matrix by which other elements are divided in an algorithm such as Gauss-Jordan elimination is called the pivot element. Partial pivoting is ...

If a circular pizza is divided into 8, 12, 16, ... slices by making cuts at equal angles from an arbitrary point, then the sums of the areas of alternate slices are equal. ...

For n points in the plane, there are at least N_1=sqrt(n-3/4)-1/2 different distances. The minimum distance can occur only <=3n-6 times, and the maximum distance can occur ...

A point p on a regular surface M in R^3 is said to be planar if the Gaussian curvature K(p)=0 and S(p)=0 (where S is the shape operator), or equivalently, both of the ...

Let (xi_1,xi_2) be a locally Euclidean coordinate system. Then ds^2=dxi_1^2+dxi_2^2. (1) Now plug in dxi_1=(partialxi_1)/(partialx_1)dx_1+(partialxi_1)/(partialx_2)dx_2 (2) ...

Consider n intersecting ellipses. The maximal number of regions into which these divide the plane are N(n)=2n^2-2n+2=2(n^2-n+1), giving values for n=1, 2, ... of 2, 6, 14, ...

The maximal number of regions into which n lines divide a plane are N(n)=1/2(n^2+n+2) which, for n=1, 2, ... gives 2, 4, 7, 11, 16, 22, ... (OEIS A000124), the same maximal ...

The Plateau curves were studied by the Belgian physicist and mathematician Joseph Plateau. They have Cartesian equation x = (asin[(m+n)t])/(sin[(m-n)t]) (1) y = ...