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| <div class="thumbinner" style="line-height: 800%"><span style="font-size: 800%;">∇</span>
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| <div class="thumbcaption">The nabla symbol</div>
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| [[image:Harp.png|right|thumb|256px|The [[harp]], the instrument after which the nabla symbol is named]]
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| '''Nabla''' is the [[symbol]] <math>\nabla</math> (∇). The name comes from the [[Greek language|Greek]] word for a Hebrew [[harp]], called the [[Nevel (instrument)|Nevel]], which had a similar shape. The symbol was first used by [[William Rowan Hamilton]] in the form of a sideways wedge: <span style="font-size: 200%">⊲</span>.
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| The nabla symbol is available in standard HTML as <code>&nabla;</code> and in [[LaTeX]] as <code>\nabla</code>. In [[Unicode]], it is the character at [[code point]] U+2207, or 8711 in [[decimal]] notation.
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| ==Use in mathematics==
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| Nabla is used in [[mathematics]] to denote the [[del]] operator, a differential operator that indicates taking [[gradient]], [[divergence]], or [[Curl (mathematics)|curl]]. It also can refer to a [[connection (mathematics)|connection]] in [[differential geometry]] and to the [[Finite difference#Forward, backward, and central differences|backward difference operator]] in the [[Finite difference#Calculus of finite differences|calculus of finite differences]], as well as the ''all'' relation (most commonly in [[lattice theory]]). It was introduced by the [[Ireland|Irish]] mathematician and physicist [[William Rowan Hamilton]] in 1837.<ref>W. R. Hamilton, in ''Trans. R. Irish Acad.'' XVII. 236 (1837)</ref> [[William Thomson, 1st Baron Kelvin|William Thomson]] wrote in 1884: "I took the liberty of asking Professor Bell whether he had a name for this symbol <math>\nabla</math> and he has mentioned to me ''nabla'', a humorous suggestion of [[James Clerk Maxwell|Maxwell]]'s. It is the name of an Egyptian harp, which was of that shape".<ref>W. Thomson, ''Notes Lect. Molecular Dynamics & Wave Theory of Light'' at Johns Hopkins Univ. x 112 (MS) (1884)</ref>
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| In 1901, [[Josiah Willard Gibbs]] and [[Edwin Bidwell Wilson]] wrote: "This symbolic operator <math>\nabla</math> 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 <math>\nabla</math> occurs a number of times, no inconvenience to the speaker or listener arises from the repetition. <math>\nabla</math>''V'' is read simply as 'del ''V''' ".<ref>Gibbs & Wilson, ''Vector analysis: a text-book for the use of students of mathematics and physics, founded upon the lectures of J. Willard Gibbs by Edwin Bidwell Wilson'' (1901)</ref>
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| ==Use in naval engineering (or [[naval architecture]])==
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| Nabla is used in naval engineering (ship design) to designate the volume [[Displacement (fluid)|displacement]] of a ship or any other waterborne vessel. Where its counterpart, the Greek [[Delta (letter)|delta]], is used to designate weight displacement (the total weight of water displaced by the ship), the nabla is used to designate volume displacement, or the total volume of water displaced by the ship in units of length cubed.
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| ==See also==
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| *[[Del]], the vector differential operator
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| *[[Del in cylindrical and spherical coordinates]]
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| *[[Gradient|grad]], [[Divergence|div]], and [[Curl (mathematics)|curl]], differential operators defined using del
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| *the [[Covariant derivative]], a separate (and tensorial) differential operator defined for [[tensors]]
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| ==Footnotes==
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| <div style="font-size: 95%">
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| <!--See [[Wikipedia:Footnotes]] for an explanation of how to generate footnotes using the <ref(erences/)> tags-->
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| <references/>
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| </div>
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| ==External links==
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| *[http://www.mat.univie.ac.at/~neum/contrib/nabla.txt History of Nabla]
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| *[http://hdl.handle.net/2027.42/7869 A survey of the improper use of ∇ in vector analysis] (1994) Tai, Chen
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| {{DEFAULTSORT:Nabla Symbol}}
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| [[Category:Mathematical symbols]]
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| [[Category:Differential operators]]
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| [[es:Nabla]]
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| [[fr:Nabla]]
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| [[nl:Nabla]]
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| [[pt:Nabla]]
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| [[sl:nabla]]
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| [[zh:劈形算符]]
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