The icosian calculus is a non-commutative algebraic structure discovered by the Irish mathematician William Rowan Hamilton in 1856.[1][2] In modern terms, he gave a group presentation of the icosahedral rotation group by generators and relations.
Hamilton's discovery derived from his attempts to find an algebra of "triplets" or 3-tuples that he believed would reflect the three Cartesian axes. The symbols of the icosian calculus can be equated to moves between vertices on a dodecahedron. Hamilton's work in this area resulted indirectly in the terms Hamiltonian circuit and Hamiltonian path in graph theory.[3] He also invented the icosian game as a means of illustrating and popularising his discovery.
- ^ William Rowan Hamilton (1856). "Memorandum respecting a new System of Roots of Unity" (PDF). Philosophical Magazine. 12: 446.
- ^ Thomas L. Hankins (1980). Sir William Rowan Hamilton. Baltimore: The Johns Hopkins University Press. p. 474. ISBN 0-8018-6973-0.
- ^ Norman L. Biggs; E. Keith Lloyd; Robin J. Wilson (1976). Graph theory 1736–1936. Oxford: Clarendon Press. p. 239. ISBN 0-19-853901-0.
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