Nabla symbol

∇ The nabla symbol The nabla is a triangular symbol resembling an inverted Greek delta: or ∇. The name comes, by reason of the symbol's shape, from the Hellenistic Greek word νάβλα for a Phoenician harp, and was suggested by the encyclopedist William Robertson Smith to Peter Guthrie Tait in correspondence. The nabla symbol is available in standard HTML as ∇ and in LaTeX as \nabla. In Unicode, it is the character at code point U+2207, or 8711 in decimal notation, in the Mathematical Operators block. It is also called del. The differential operator given in Cartesian coordinates on three-dimensional Euclidean space by was introduced in 1837 by the Irish mathematician and physicist William Rowan Hamilton, who called it ◁. (The unit vectors were originally right versors in Hamilton's quaternions.) The mathematics of ∇ received its full exposition at the hands of P. G. Tait. After receiving Smith's suggestion, Tait and James Clerk Maxwell referred to the operator as nabla in their extensive private correspondence; most of these references are of a humorous character. C. G. Knott's Life and Scientific Work of Peter Guthrie Tait (p. 145): It was probably this reluctance on the part of Maxwell to use the term Nabla in serious writings which prevented Tait from introducing the word earlier than he did. The one published use of the word by Maxwell is in the title to his humorous Tyndallic Ode, which is dedicated to the "Chief Musician upon Nabla", that is, Tait. William Thomson (Lord Kelvin) introduced the term to an American audience in an 1884 lecture; the notes were published in Britain and the U.S. in 1904. The name is acknowledged, and criticized, by Oliver Heaviside in 1891: The fictitious vector ∇ given by is very important. Physical mathematics is very largely the mathematics of ∇. The name Nabla seems, therefore, ludicrously inefficient. Heaviside and Josiah Willard Gibbs (independently) are credited with the development of the version of vector calculus most popular today.