The Icosian Calculus is a non-commutative algebraic structure discovered by the Irish mathematician William Rowan Hamilton in 1856. In modern terms, he gave a group presentation of the icosahedral 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.

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  • The Icosian Calculus is a non-commutative algebraic structure discovered by the Irish mathematician William Rowan Hamilton in 1856. In modern terms, he gave a group presentation of the icosahedral 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. He also invented the Icosian Game as a means of illustrating and popularising his discovery.
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  • The Icosian Calculus is a non-commutative algebraic structure discovered by the Irish mathematician William Rowan Hamilton in 1856. In modern terms, he gave a group presentation of the icosahedral 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.
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  • Icosian Calculus
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