Hamilton's Research on Quaternions

The fundamental formula

i² = j² = k² = ijk = -1

Hamilton described the train of thought that led to his discovery in a letter to John T. Graves, who had been a fellow student with Hamilton at Trinity College, Dublin.

On the 13th November, 1843 he presented a paper, On a new Species of Imaginary Quantities connected with a theory of Quaternions , at a meeting of the Royal Irish Academy describing his discovery.

Almost a year later, on the 11th November, 1844, he presented another paper, On Quaternions, at a meeting of the Royal Irish Academy.

A full account of Hamilton's early research on quaternions is to be found in the paper Researches respecting Quaternions, First Series , which was published in volume 21 of the Transactions of the Royal Irish Academy

Hamilton subsequently published many papers developing the theory of quaternions, including a substantial paper On Quaternions, or on a New System of Imaginaries in Algebra , published in installments in the Philosophical Magazine in between 1844 and 1850. He also developed a `coordinate-free' approach to the subject in another paper, On Symbolical Geometry , which appeared in installments in the Cambridge and Dublin Mathematical Journal between 1846 and 1849. His Lectures on Quaternions were published in 1853. (This book has 736 pages.) A second book, the Elements of Quaternions was almost complete at the time of his death.

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