In 2005 a mathematics student called Mary Radcliffe developed the concept of a puzzle she called Planarity. It was implemented as a computer game on the internet by John Tantalo. The idea is to take an undirected graph, and the puzzle is to place the vertices (‘nodes’) in such a way that the graph is planar, i.e. the the edges (‘lines’) do not cross. A graph (drawn in 2D) without crossing edges is called a planar graph in mathematics, and this suggested name Planarity. It is an old problem in mathematics how to quickly determine whether a graph is planer or not.

The game became somewhat of a craze among the flash-based gaming community under the name Untangle (just google for “untangle game” and you will find dozens of implementations). Unexpectedly, the game is also available on the iPhone.