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Icosian calculus, the Glossary

Index Icosian calculus

The icosian calculus is a non-commutative algebraic structure discovered by the Irish mathematician William Rowan Hamilton in 1856.[1]

Table of Contents

  1. 24 relations: Algebraic structure, Alternating group, Associative property, Combinatorial group theory, Commutative property, Coxeter group, Dessin d'enfant, Directed graph, Dodecahedron, Generating set of a group, Geometric group theory, Group (mathematics), Hamiltonian path, Icosahedral symmetry, Icosahedron, Icosian, Icosian game, Philosophical Magazine, Presentation of a group, Root of unity, Séminaire Lotharingien de Combinatoire, Triangle group, Tuple, William Rowan Hamilton.

  2. Binary operations
  3. William Rowan Hamilton

Algebraic structure

In mathematics, an algebraic structure consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities, known as axioms, that these operations must satisfy. Icosian calculus and algebraic structure are abstract algebra.

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Alternating group

In mathematics, an alternating group is the group of even permutations of a finite set.

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Associative property

In mathematics, the associative property is a property of some binary operations that means that rearranging the parentheses in an expression will not change the result.

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Combinatorial group theory

In mathematics, combinatorial group theory is the theory of free groups, and the concept of a presentation of a group by generators and relations.

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Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

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Coxeter group

In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors).

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Dessin d'enfant

In mathematics, a dessin d'enfant is a type of graph embedding used to study Riemann surfaces and to provide combinatorial invariants for the action of the absolute Galois group of the rational numbers.

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Directed graph

In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs. Icosian calculus and directed graph are graph theory.

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Dodecahedron

In geometry, a dodecahedron or duodecahedron is any polyhedron with twelve flat faces.

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Generating set of a group

In abstract algebra, a generating set of a group is a subset of the group set such that every element of the group can be expressed as a combination (under the group operation) of finitely many elements of the subset and their inverses.

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Geometric group theory

Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups can act non-trivially (that is, when the groups in question are realized as geometric symmetries or continuous transformations of some spaces).

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Group (mathematics)

In mathematics, a group is a set with an operation that associates an element of the set to every pair of elements of the set (as does every binary operation) and satisfies the following constraints: the operation is associative, it has an identity element, and every element of the set has an inverse element.

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Hamiltonian path

In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. Icosian calculus and Hamiltonian path are William Rowan Hamilton.

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Icosahedral symmetry

In mathematics, and especially in geometry, an object has icosahedral symmetry if it has the same symmetries as a regular icosahedron. Icosian calculus and icosahedral symmetry are Rotational symmetry.

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Icosahedron

In geometry, an icosahedron is a polyhedron with 20 faces.

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Icosian

In mathematics, the icosians are a specific set of Hamiltonian quaternions with the same symmetry as the 600-cell.

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Icosian game

The icosian game is a mathematical game invented in 1856 by Irish mathematician William Rowan Hamilton. Icosian calculus and icosian game are graph theory and William Rowan Hamilton.

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Philosophical Magazine

The Philosophical Magazine is one of the oldest scientific journals published in English.

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Presentation of a group

In mathematics, a presentation is one method of specifying a group.

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Root of unity

In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that yields 1 when raised to some positive integer power.

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Séminaire Lotharingien de Combinatoire

The Séminaire Lotharingien de Combinatoire (English: Lotharingian Seminar of Combinatorics) is a peer-reviewed academic journal specialising in combinatorial mathematics, named after Lotharingia.

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Triangle group

In mathematics, a triangle group is a group that can be realized geometrically by sequences of reflections across the sides of a triangle.

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Tuple

In mathematics, a tuple is a finite sequence or ordered list of numbers or, more generally, mathematical objects, which are called the elements of the tuple.

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William Rowan Hamilton

Sir William Rowan Hamilton (3/4 August 1805 – 2 September 1865) was an Irish mathematician, astronomer, and physicist.

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See also

Binary operations

William Rowan Hamilton

References

[1] https://en.wikipedia.org/wiki/Icosian_calculus