| Dedicated to the Memory of Sir William Rowan Hamilton | |||||||||||||||
| History | |||||||||||||||
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"In 1857 the famous Irish
mathematician Sir William Rowan Hamilton invented a game which used a solid regular
dodecahedron (a geometric object having 20 vertices, 30 edges, and 12 faces), 20 pegs (one
inserted at each vertex), and a supply of string. (Since the dodecahedron has 12 faces, it
makes an ideal desk calendar.) Every vertex was given the name of an important city of the
time. The object of the game, called Around the World, was to find a
route along the edges of the dodecahedron that visits every city exactly once and
terminates where it began. In order for the player to keep track of the cities visited,
the player used the string to join pegs in the order in which the route proceeded. This
dodecahedron did not prove very popular, so Hamilton also produced a two-dimensional
version of the game (see Figure). Apparently, neither version of the game was successful,
possibly because a desired route can be found rather easily. Although graphs with spanning cycles are named for Hamilton, he was not the first to have this idea. Two years before Hamilton introduced his game, T. P. Kirkman posed the following question in a paper which he submitted to the Royal Society of England: Given a graph of a polyhedron, does there exist a cycle passing through every vertex?" Gary Chartrand, Ortrud R. Oellermann, Applied and
algorithmic graph theory. McGraw-Hill (1993). |
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Keywords: graph,
hamilton, locality, stability.
Last modified 2001-02-26. Page master Nikolay K. Khachatryan. |
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