| His work in algebraic number theory led him to study the quaternions and generalisations such as Clifford algebras. |
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| Later on, in 1858, Bellavitis included the system of quaternions into his geometric calculus. |
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| Shortly after Hamilton's discovery of the quaternions his personal life started to prey on his mind again. |
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| I have been able to get a sort of visualizable flash of insight in 4 dimensions, when I had been thinking about quaternions for over a month for 8 hours a day. |
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| Hurwitz published a paper on a factorisation theory for integer quaternions in 1896 and applied it to the problem of representing an integer as the sum of four squares. |
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| Notable mathematicians include Sir William Rowan Hamilton, famous for work in classical mechanics and the invention of quaternions. |
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| It was while he was a pupil at the bar examination that he went to Dublin to hear Hamilton's lectures on quaternions. |
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| Maxwell expressed electromagnetism in the algebra of quaternions and made the electromagnetic potential the centrepiece of his theory. |
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| A few years later there was a debate between Heaviside and Peter Guthrie Tait about the relative merits of vector analysis and quaternions. |
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| The triads and quaternions with which he loaded his sentences. |
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| If the desired result is to perform the smallest possible rotation between each pair of two orientations, you can preprocess the quaternions to achieve this. |
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| He has also done work in algebra, particularly with quaternions. |
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