He founded a school of 'quaternionists', and he tried to popularize quaternions in several books. Hamilton's treatment is more geometric than the modern approach, which emphasizes quaternions' algebraic properties. Hamilton called a quadruple with these rules of multiplication a quaternion, and he devoted most of the remainder of his life to studying and teaching them. An electric circuit seemed to close, and a spark flashed forth. This letter was later published in a letter to the London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science Hamilton states:Īnd here there dawned on me the notion that we must admit, in some sense, a fourth dimension of space for the purpose of calculating with triples. Graves, describing the train of thought that led to his discovery. On the following day, Hamilton wrote a letter to his friend and fellow mathematician, John T. Although the carving has since faded away, there has been an annual pilgrimage since 1989 called the Hamilton Walk for scientists and mathematicians who walk from Dunsink Observatory to the Royal Canal bridge in remembrance of Hamilton's discovery. Into the stone of Brougham Bridge as he paused on it. Quaternions are generally represented in the formĪ + b i + c j + d k, Multiplication of quaternions is noncommutative. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space, or, equivalently, as the quotient of two vectors. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. In mathematics, the quaternion number system extends the complex numbers. (If the image is opened in the Wikipedia commons by clicking twice on it, cycles can be highlighted by hovering over or clicking on them.) Top row shows the post-multiplier.)Ĭayley Q8 graph showing the six cycles of multiplication by i, j and k. Note: This is a multiplication table, not a Cayley table, because inverses do not appear in the row or column headings. For other uses, see Quaternion (disambiguation). This article is about quaternions in mathematics.

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