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Nabla is the symbol
Symbol

A symbol is something such as an entity, picture, written word, sound, or particular mark that represents something else by association, resemblance, or convention....
 . The name comes from the Greek
Greek language

Greek is an Indo-European languages native to the southern Balkan peninsula, the language of the Greek people. It forms an independent branch within Indo-European....
 word for a Hebrew harp
Harp

The 'harp' is a stringed instrument which has the plane of its strings positioned perpendicular to the Sounding board. It is also considered to be a percussion instrument....
, which had a similar shape. Related words also exist in Aramaic
Aramaic language

Aramaic is a Semitic languages with a 3,000-year history. It has been the language of administration of empires and the language of divine worship....
 and Hebrew
Hebrew language

Hebrew is a Semitic languages of the Afro-Asiatic languages. Modern Hebrew is spoken by more than seven million people in Israel and Classical Hebrew is used for prayer or study in Jews communities around the world....
. The symbol was first used by William Rowan Hamilton
William Rowan Hamilton

Sir William Rowan Hamilton was an Ireland physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra....
 in the form of a sideways wedge: ?. Another, less-common name for the symbol is atled (delta spelled backwards), because the nabla is an inverted Greek letter
Greek alphabet

The Greek alphabet is a set of twenty-four letters that has been used to write the Greek language since the late 9th century BC or early 8th century BCE....
 delta
Delta (letter)

Delta is the fourth letter of the Greek alphabet. In the system of Greek numerals it has a value of 4. It was derived from the Phoenician alphabet Dalet , but in the Ancient Greek language, it represented a voiced dental plosive ....
.






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Harp
Nabla is the symbol
Symbol

A symbol is something such as an entity, picture, written word, sound, or particular mark that represents something else by association, resemblance, or convention....
 . The name comes from the Greek
Greek language

Greek is an Indo-European languages native to the southern Balkan peninsula, the language of the Greek people. It forms an independent branch within Indo-European....
 word for a Hebrew harp
Harp

The 'harp' is a stringed instrument which has the plane of its strings positioned perpendicular to the Sounding board. It is also considered to be a percussion instrument....
, which had a similar shape. Related words also exist in Aramaic
Aramaic language

Aramaic is a Semitic languages with a 3,000-year history. It has been the language of administration of empires and the language of divine worship....
 and Hebrew
Hebrew language

Hebrew is a Semitic languages of the Afro-Asiatic languages. Modern Hebrew is spoken by more than seven million people in Israel and Classical Hebrew is used for prayer or study in Jews communities around the world....
. The symbol was first used by William Rowan Hamilton
William Rowan Hamilton

Sir William Rowan Hamilton was an Ireland physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra....
 in the form of a sideways wedge: ?. Another, less-common name for the symbol is atled (delta spelled backwards), because the nabla is an inverted Greek letter
Greek alphabet

The Greek alphabet is a set of twenty-four letters that has been used to write the Greek language since the late 9th century BC or early 8th century BCE....
 delta
Delta (letter)

Delta is the fourth letter of the Greek alphabet. In the system of Greek numerals it has a value of 4. It was derived from the Phoenician alphabet Dalet , but in the Ancient Greek language, it represented a voiced dental plosive ....
. In actual Greek usage, the symbol is called a??de?ta, anádelta, which means "upside-down delta".

The nabla symbol is available in standard HTML as ∇ and in LaTeX
LaTeX

LaTeX is a document markup language and Word processor for the TeX typesetting program. Within the typesetting system, its name is styled as ....
 as \nabla. In Unicode
Unicode

Unicode is a computing industry standard allowing computers to consistently represent and manipulate Character expressed in most of the world's writing systems....
, it is the character at code point
Code point

In character encoding terminology a code point is any of the numerical values that make up the codespace. For example, ASCII comprises 128 code points in the range 0Hexadecimal to 7Fhex, Extended ASCII comprises 256 code points in the range 0Hexadecimal to FFhex, and Unicode comprises 1,114,112 code...
 U+2207, or 8711 in decimal
Decimal

The decimal numeral system has 10 as its Base . It is the most widely used numeral system....
 notation.

Use in mathematics

Nabla is used in mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
 to denote the del
Del

In vector calculus, del is a vector differential operator represented by the nabla symbol: .Del is a mathematical tool serving primarily as a Convention for mathematical notation; it makes many equations easier to comprehend, write, and remember....
 operator. It also can refer to a connection
Connection (mathematics)

In geometry, the notion of a connection makes precise the idea of transporting data along a curve or family of curves in a parallel and consistent manner....
 in differential geometry, as well as the all relation (most commonly in lattice theory). It was introduced by the Irish
Ireland

Ireland is the List of islands by area in Europe, and the twentieth-largest island in the world. It lies to the north-west of continental Europe and is surrounded by hundreds of islands and islet....
 mathematician and physicist William Rowan Hamilton in 1837 . William Thomson
William Thomson, 1st Baron Kelvin

William Thomson, 1st Baron Kelvin , Order of Merit , Royal Victorian Order, Privy Council of the United Kingdom, Presidents of the Royal Society, Royal Society of Edinburgh, was an Ireland-born United Kingdom of Great Britain and Ireland Mathematical physics and engineer....
 wrote in 1884: "I took the liberty of asking Professor Bell whether he had a name for this symbol and he has mentioned to me nabla, a humorous suggestion of Maxwell
James Clerk Maxwell

James Clerk Maxwell was a Scotland Mathematical physics. His most significant achievement was the development of the classical electromagnetic theory, synthesizing all previous unrelated observations, experiments and equations of electricity, magnetism and even optics into a consistent theory....
's. It is the name of an Egyptian harp, which was of that shape".

In 1901, Josiah Willard Gibbs
Josiah Willard Gibbs

Josiah Willard Gibbs was an American theoretical physicist, chemist, and mathematician. One of the greatest American scientists of all time, he devised much of the theoretical foundation for chemical thermodynamics as well as physical chemistry....
 and Edwin Bidwell Wilson
Edwin Bidwell Wilson

Edwin Bidwell Wilson was an American mathematician and polymath. He was the sole proteg? of Yale's physicist Josiah Willard Gibbs and was mentor to Harvard economist Paul Samuelson....
 wrote: "This 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 ".

See also


  • Del
    Del

    In vector calculus, del is a vector differential operator represented by the nabla symbol: .Del is a mathematical tool serving primarily as a Convention for mathematical notation; it makes many equations easier to comprehend, write, and remember....
    , the vector differential operator
  • Del in cylindrical and spherical coordinates
    Del in cylindrical and spherical coordinates

    This is a list of some vector calculus formulae of general use in working with various coordinate systems.See also * Orthogonal coordinates...
  • grad
    Gradient

    In vector calculus, the gradient of a scalar field is a vector field which points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....
    , div
    Divergence

    In vector calculus, the divergence is an operator that measures the magnitude of a vector field's source or sink at a given point; the divergence of a vector field is a scalar....
    , and curl, differential operators defined using del
  • the Covariant derivative
    Covariant derivative

    In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a differential operator, to be contrasted with the approach given by a connection on the frame bundle &mdas...
    , a separate (and tensorial) differential operator defined for tensors


Footnotes


External links


  • (1994) Tai, Chen