Nabla symbol

The nabla is a triangular symbol like an inverted Greek delta: ∇ {displaystyle abla } 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.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.The fictitious vector ∇ given byThis symbolic operator ∇ was introduced by Sir W. R. Hamilton and is now in universal employment. There seems, however, to be no universally recognized name for it, although owing to the frequent occurrence of the symbol some name is a practical necessity. It has been found by experience that the monosyllable del is so short and easy to pronounce that even in complicated formulae in which ∇ occurs a number of times, no inconvenience to the speaker or listener arises from the repetition. ∇V is read simply as ‘del V’.My dear Sir, The name I propose for ∇ is, as you will remember, Nabla... In Greek the leading form is ναβλᾰ... As to the thing it is a sort of harp and is said by Hieronymus and other authorities to have had the figure of ∇ (an inverted Δ).Unquestionably, however, Tait's great work was his development of the powerful operator ∇. Hamilton introduced this differential operator in its semi-Cartesian trinomial form on page 610 of his Lectures and pointed out its effects on both a scalar and a vector quantity. ... Neither in the Lectures nor in the Elements, however, is the theory developed. This was done by Tait in the second edition of his book (∇ is little more than mentioned in the first edition) and much more fully in the third and last edition.I took the liberty of asking Professor Ball two days ago whether he had a name for this symbol ∇2, and he has mentioned to me nabla, a humorous suggestion of Maxwell's. It is the name of an Egyptian harp, which was of that shape. I do not know that it is a bad name for it. Laplacian I do not like for several reasons both historical and phonetic. As this is written, he appears to be naming the Laplacian ∇2 'nabla', but in the lecture was presumably referring to ∇ itself. We can represent cases of this form, cases where it is indeterminate whether in fiction f: a=b, as follows:(A) ∇f. The nabla is a triangular symbol like an inverted Greek delta: ∇ {displaystyle abla } 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 abla. In Unicode, it is the character at code point U+2207, or 8711 in decimal notation. It is also called del. The differential operator given in Cartesian coordinates { x , y , z } {displaystyle {x,y,z}} 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 { i , j , k } {displaystyle {mathbf {i} ,mathbf {j} ,mathbf {k} }} were originally Hamilton's unit 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): 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: Heaviside and Josiah Willard Gibbs (independently) are credited with the development of the version of vector calculus most popular today.