Icosian Game

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The Icosian Game ( Greek είκοσι eikosi , German 'twenty' ) is a board game for two people from 1857 by the mathematician William Rowan Hamilton . Nowadays it is mainly known for the fact that this is the first time that the question of a circular route through all corners of a graph is asked, which is now known as the Hamilton circle .

history

During his mathematical work on algebra , Hamilton discovered that there is a circular path through all corners of a dodecahedron . On the advice of his friend John Thomas Graves , he developed a game out of it, the Icosian Game . He sold the rights to it in 1857 for £ 25  to the major game manufacturer John Jaques & Son , who marketed the game.

A variant based on the same game principle was published in 1859 under the title The Traveller's Dodecahedron .

From an economic point of view, the games were not a great success, only a few copies were sold, correspondingly few copies have survived to this day.

However, the games were the subject of scientific essays and, above all, works on entertainment mathematics. Both Édouard Lucas and Wilhelm Ahrens each dedicated a separate chapter to the game in their works on entertainment mathematics. Also WW Rouse Ball analyzed the game, and Martin Gardner dealt in one of his Mathematical Games-columns with the game.

game

Schedule of the Icosian Game

The Icosian Game consists of a game board and twenty pieces . The board has twenty indentations, these are marked with the consonants and connected by lines in such a way that the Schlegel diagram of a dodecahedron results. The stones are numbered from 1 to 20 and can be inserted into the recesses of the board.

In each round, one of the two players must place all or a certain part of the pieces on the board, observing certain rules. The pieces must always be placed in such a way that the resulting path follows the given lines. The other player can, however, demand further additional conditions.

As a first example, the rules of the game name the following task: The first player places the stones with the numbers 1 to 5 in five consecutive wells, the second player should continue the path with the remaining stones in such a way that it becomes cyclical, i.e. stone 20 finally next to the number 1.

The rules provide further examples so that the game can also be played alone.

Hamilton circle through all corners of a dodecahedron

The Traveller's Dodecahedron follows the same principle, but instead of a game board there is an irregular dodecahedron that can be mounted and held on a stick. The path is not marked with game pieces, but with a cord that is wrapped around pins that are attached to the twenty corners. In addition, the names of cities are assigned to the corners in the instructions, with their first letters again being the twenty consonants. These changes made the original abstract game into a much more accessible version.

Individual evidence

  1. ^ David Darling: Icosian Game. Retrieved April 9, 2019 .
  2. ^ Mathematical games. Retrieved April 9, 2019 .
  3. ↑ James Dalgety: Sir William Hamilton's Icosian Game and Traveller's Dodecahedron Puzzle. Retrieved April 9, 2019 .
  4. ↑ AS Herschel: Sir Wm. Hamilton's Icosian Game . In: The quarterly journal of pure and applied mathematics . Parker, 1862, p. 305 (English, uni-goettingen.de ).
  5. ^ Peter Guthrie Tait: Listing's Topology . In: The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science . tape 17 , no. 103 , January 1884, ISSN  1941-5982 , pp. 30-46 , here p. 42 , doi : 10.1080 / 14786448408627475 .
  6. ^ Édouard Lucas: Récréations mathématiques . tape 2 . Gauthier-Villars, Paris 1892, p. 199-227 ( archive.org ).
  7. ^ Wilhelm Ahrens: Mathematical conversations and games . BG Teubner, Leipzig 1901, p. 327-339 ( bnf.fr ).
  8. ^ WW Rouse Ball: Mathematical Recreations and Essays . 1926, p. 189-192 ( archive.org ).
  9. ^ Martin Gardner: About the remarkable similarity between the Icosian Game and the Tower of Hanoi . In: Scientific American . May 1957.
  10. ^ Rules of the game, reprinted in: Norman Biggs, E. Keith Lloyd, Robin J. Wilson: Graph Theory, 1736–1936 . Clarendon Press, 1986, ISBN 978-0-19-853916-2 , pp. 32–33 ( limited preview in Google Book search).

Web links