The Hamiltonian


Inspired by a game devised by the Irish mathematician Sir William Rowan Hamilton in 1859, the Hamiltonian Circuit is based on graph theory. Think of it as a giant maze. To create the circuit, you have to visit each vertex in the grid exactly once, never going backwards or crossing a path.

There is only ever one solution per circuit. The more complex the circuit, the harder it is to solve—like this one, for instance.  

On October 16, 1843, when Hamilton was thinking of ways to extend complex numbers to higher spatial dimensions, he began working in four dimensions, and in doing so, discovered quaternions. The actual equation came to him at an inopportune time; he was walking along the Royal Canal in Dublin with his wife, and with nothing else to write on, he took out his penknife and carved it into the side of the nearby Broom Bridge. Although his original carving is gone, this plaque was placed there in his honor on November 13, 1958, by Taoiseach Eamon de Valera, a mathematician and student of quaternions.
i2 = j2 = k2 = ijk = −1