Nabla
∇



Mathematical signs  
arithmetic  
Plus sign  + 
Minus sign   , ./. 
Mark  ⋅ , × 
Divided sign  : , ÷ , / 
Plus minus sign  ± , ∓ 
Comparison sign  < , ≤ , = , ≥ , > 
Root sign  √ 
Percent sign  % 
Analysis  
Sum symbol  Σ 
Product mark  Π 
Difference sign , Nabla  ∆ , ∇ 
Prime  ′ 
Partial differential  ∂ 
Integral sign  ∫ 
Concatenation characters  ∘ 
Infinity symbol  ∞ 
geometry  
Angle sign  ∠ , ∡ , ∢ , ∟ 
Vertical , parallel  ⊥ , ∥ 
Triangle , square  △ , □ 
Diameter sign  ⌀ 
Set theory  
Union , cut  ∪ , ∩ 
Difference , complement  ∖ , ∁ 
Element character  ∈ 
Subset , superset  ⊂ , ⊆ , ⊇ , ⊃ 
Empty set  ∅ 
logic  
Follow arrow  ⇒ , ⇔ , ⇐ 
Universal quantifier  ∀ 
Existential quantifier  ∃ 
Conjunction , disjunction  ∧ , ∨ 
Negation sign  ¬ 
The symbol Nabla (∇) is a mathematical symbol that is mainly used in vector analysis to denote the Nabla operator . In addition, it is used in differential geometry to denote the relationship or the covariant derivative .
description
The symbol Nabla is not a letter, but arose from similar symbols of the quaternion analysis by William Rowan Hamilton . Peter Guthrie Tait introduced today's form of an upsidedown delta Δ. The name "Nabla" comes from the theologian William Robertson Smith (18461894), who derived the form from the biblical lyre Nevel ( Hebrew נבל nével , ancient Greek νάβλα nábla , Latin nablium ).
The Nabla is identical to the symbol for water in the ancient fourelement teaching . However, there is neither a substantive nor a historical relationship between the two symbols.
The character Nabla can be represented in HTML as ∇
and in LaTeX as \nabla
. In the Unicode character set, it has the symbol number 8711 ( hexadecimal 0x2207).
use
 In vector analysis , the Nabla operator is used for the vector representation of the differential operators for the gradient , the divergence and the rotation .
 In differential geometry , the symbol is used for affine relationships .
 In shipbuilding , Nabla symbolizes the structural displacement in cubic meters.
 In the APL programming language , the character starts and ends
∇
the line editor for functions and, as a functional symbol, has the meaning of selfreference . Furthermore, the Nabla is part of some compound APL symbols such as⍒
and⍫
.  In microbiology / bioprocess engineering , Nabla denotes the sterility criterion .
Individual evidence
 ^ Manfredo Perdigão do Carmo: Riemannian Geometry. Birkhäuser, Boston 1992, ISBN 0817634908 , p. 50.
 ↑ Capt. DRDerret, Dr. CBBarrass: Ship Stability for Masters and Mates Elsevier ButterworthHeinemann, 5th Edition, ISBN 0750641010 , p. 378.
 ↑ Dubasi Govardhana Rao: Introduction to Biochemical Engineering . Tata McGrawHill Education, 2010, ISBN 9780070151383 ( google.de [accessed February 7, 2019]).