A trick of the hat — finding the elusive einstein tile
A nearly 60-year-old mathematical problem has finally been solved.
The story began last fall when David Smith, a retired print technician from Yorkshire, England, came upon a shape with a tantalizing property. The life-long tiling enthusiast discovered a 13-sided shape — dubbed the hat — that is able to fill the infinite plane without overlaps or gaps in a pattern that not only never repeats but also never can be made to repeat.