Even the most brilliant innovators get their inspiration from somewhere. For the Dutch graphic artist M.C. Escher, such a creative impetus came from a particular illustration in a 1957 mathematical ...

Tessellations aren’t just eye-catching patterns—they can be used to crack complex mathematical problems. By repeatedly reflecting shapes to tile a surface, researchers uncovered a method that links ...

A novel map of the internet created by Marián Boguñá and colleagues at the University of Barcelona, Spain, could help make network glitches a thing of the past. Boguñá squeezed the entire network into ...

In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space. When you gaze out ...

In mathematics, hyperbolic geometry is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is rejected. The parallel postulate in Euclidean geometry states, for two ...