"Given a subset K of the unit Euclidean sphere, we estimate the minimal number m = m(K) of hyperplanes that generate a uniform tessellation of K, in the sense that the fraction of the hyperplanes separating any pair x,y in K is nearly proportional to the Euclidean distance between x and y. Random hyperplanes prove to be almost ideal for this problem; they achieve the almost optimal bound m = O(w(K)^2) where w(K) is the Gaussian mean width of K."

Collectively, Nathan Allan Glass Studios Inc. is an artist, and glass is their canvas. The Canada-based company produces glass in dozens of unique textures, and the company's focus on R&D aims to retain an innovative and competitive edge by coming up with surfaces that others cannot.

This Your Superfund project is testing out a new trick – doing nearest-neighbor queries with UTFGrid.

teaching tool to demonstrate and explore tesselations, patterns and rotation. primary years

pattern

By the year 1200 C.E. a conceptual breakthrough occurred in which girih patterns were reconceived as tessellations of a special set of equilateral polygons (“girih tiles”) decorated with lines - 700 years before western mathematics.

I never realized there was such a thing as origami tesselations... though I'm constantly finding myself turning flat paper into 3d designs. Something I'm going to have to try

"In the Grotesque we see symmetry, movement, and purpose, signs of life where there ought not to be any." Lots of really interesting examples.