work, in 1840 Benjamin Olinde Rodrigues had reached a result that amounted to their discovery in all but name. Hamilton was looking for ways of extending complex numbers (which can be viewed as points on a 2-dimensional Argand diagram) to higher spatial dimensions. In working with four dimensions, rather than three, he created quaternion algebra. According to Hamilton, on 16 October he was out walking along the Royal Canal in Dublin with his wife when the solution in the form of the equation occurred to him; Hamilton then carved this equation using his penknife into the side of the nearby Broom Bridge (which Hamilton called Brougham Bridge). The quaternions involved abandoning the commutative law, a radical step for the time. In the context of this prototype geometric algebra, Hamilton also introduced the cross and dot products of vector algebra, the quaternion product being the cross product minus the dot product as scalar. Hamilton also described a quaternion as an ordered four-element multiple of real numbers, and described the first element as the "scalar" part, and the remaining three as the "vector" part. He coined the neologisms "tensor" and "scalar", and was the first to use the word "vector" in the modern sense. Other mathematical works Hamilton looked into the solution of the quintic in the theory of equations, examining of the results arrived at by Niels Henrik Abel, George Jerrard and others in their researches. There is Hamilton's paper on fluctuating functions in Fourier analysis, and the invention of the hodograph. Of his investigations into the solutions, especially by numerical approximation, of certain classes of physically-important differential equations, only parts were published, at intervals, in the Philosophical Magazine. Hamilton also introduced the icosian game or Hamilton's puzzle. It is based on the concept of a Hamiltonian path in graph theory. Publications Hamilton, Sir W.R. (1853), Lectures on Quaternions Dublin: Hodges and Smith Hamilton, Sir W.R., Hamilton, W.E. (ed) (1866), Elements of Quaternions London: Longmans, Green, & Co. Hamilton, W.R. (1833), Introductory Lecture on Astronomy Dublin University Review and Quarterly Magazine Vol. I, Trinity College Dublin For Hamilton's mathematical papers see David R. Wilkins, Sir William Rowan Hamilton (1805-1865): Mathematical Papers Hamilton introduced, as a method of analysis, both quaternions and biquaternions, the extension to eight dimensions by introduction of complex number coefficients. When his work was assembled in 1853, the book Lectures on Quaternions had "formed the subject of successive