Notation system

Inlinguisticsandsemiotics,anotation systemis asystemof graphics orsymbols,charactersand abbreviatedexpressions,used (for example) inartisticandscientific disciplinesto represent technical facts and quantities byconvention.^[1]^[2]Therefore, a notation is a collection of related symbols that are each given anarbitrarymeaning, created to facilitatestructured communicationwithin adomain knowledgeorfield of study.

Standard notations refer to general agreements in the way things are written or denoted. The term is generally used in technical and scientific areas of study likemathematics,physics,chemistryandbiology,but can also be seen in areas likebusiness,economicsandmusic.

Written communication

Writing systems

Phonographicwriting systems,by definition, use symbols to represent components of auditory language, i.e.speech,which in turn refers to things or ideas. The two main kinds of phonographic notational system are thealphabetand thesyllabary.Some written languages are more consistent in their correlation of written symbols (orgraphemes) with sound (orphonemes), and are therefore considered to have betterphonemic orthography.
Ideographic writing, by definition, refers to things or ideas independently of their pronunciation in any language. Some ideographic systems are alsopictogramsthat convey meaning through their pictorial resemblance to a physical object.

Linguistics

Various brackets, parentheses, slashes, and lines are used around words and letters inlinguisticsto distinguish written from spoken forms, etc. SeeInternational Phonetic Alphabet § Brackets and transcription delimiters.

Biology and medicine

Chemistry

Achemical formuladescribes a chemical compound using element symbols and subscripts, e.g.H
₂Ofor water orC
₆H
₁₂O
₆for glucose
SMILESis a notation for describing the structure of a molecule with aplain textstring, e.g. N=N for nitrogen or CCO for ethanol

Computing

BNF (Backus normal form, orBackus–Naur form) and EBNF (extended Backus-Naur form) are the two main notation techniques for context-free grammars.
Drakon-chartsare a graphical notation of algorithms and procedural knowledge.
Hungarian notationis an identifier naming convention incomputer programming,that represents thetypeor intended use of avariablewith a specific pattern within its name.
Mathematical markup languagesare computer notations for representing mathematical formulae.
Various notations have been developed to specifyregular expressions.
TheAPL programming languageprovided a rich set of very concise new notations

Logic

A variety of symbols are used to express logical ideas; see theList of logic symbols

Management

Time and motion study symbols such astherbligs

Mathematics

Mathematical notationis used to represent various kinds of mathematical ideas.
- All types ofnotation in probability
- Cartesian coordinate system,for representing position and other spatial concepts in analytic geometry
- Notation for differentiation,common representations of thederivativeincalculus
- Big O notation,used for example in analysis to represent less significant elements of an expression, to indicate that they will be neglected
- Z notation,a formal notation for specifying objects usingZermelo–Fraenkel set theoryandfirst-order predicate logic
- Ordinal notation
- Set-builder notation,a formal notation for definingsetsinset theory
Systems to represent very large numbers
- Conway chained arrow notation,an arrow system
- Knuth's up-arrow notation,an arrow system
- Steinhaus–Moser notation,Polygon Numbers
- Schläfli symbolin geometry
- Symbol Levelled notation,The Ultimate Leveller
Numeral systems,notation for writing numbers, including
- Arabic numerals
- Roman numerals
- Scientific notationfor expressing large and small numbers
- Sign-value notation,using signs or symbols to represent numbers
- Positional notationalso known as place-value notation, in which each position is related to the next by a multiplier which is called thebaseof that numeral system
  - Binary notation,a positional notation in base two
  - Octalnotation, a positional notation in base eight, used in some computers
  - Decimal notation,a positional notation in base ten
  - Hexadecimalnotation, a positional notation in base sixteen, commonly used in computers
  - Sexagesimalnotation, an ancient numeral system in base sixty
See alsoTable of mathematical symbols- for general tokens and their definitions...

Physics

Bra–ket notation,or Dirac notation, is an alternative representation of probability distributions inquantum mechanics.
Tensor index notationis used when formulating physics (particularlycontinuum mechanics,electromagnetism, relativistic quantum mechanics and field theory, and general relativity) in the language oftensors.

Typographical conventions

Infix notation,the common arithmetic and logical formula notation, such as "a+b−c".
Polish notationor "prefix notation", which places the operator before the operands (arguments), such as "+ab".
Reverse Polish notationor "postfix notation", which places the operator after the operands, such as "ab+ ".

Sports and games

Baseball scorekeeping,to represent a game of baseball
Aresti Catalogue,to represent aerobatic manoeuvres
Chess notation,to represent moves in a game of chess
Siteswapnotation represents a juggling pattern as a sequence of numbers
Singmaster notation,to represent Rubik's Cube moves

Graphical notations

Music

Musical notationpermits a composer to express musical ideas in a musical composition, which can be read and interpreted during performance by a trained musician; there are many different ways to do this (hundreds have been proposed), althoughstaff notationprovides by far the most widely used system ofmodern musical symbols.

Dance and movement

Benesh Movement Notationpermits a graphical representation of human bodily movements
Laban Movement AnalysisorLabanotationpermits a graphical representation of human bodily movements
Eshkol-Wachman Movement Notationpermits a graphical representation of bodily movements of other species in addition to humans, and indeed any kind of movement (e.g. aircraft aerobatics)
Juggling diagramsrepresent juggling patterns
Aresti aerobatic symbolsprovides a way to represent flight maneuvers in aerobatics

Science

Feynman diagramspermit a graphical representation of a perturbative contribution to the transition amplitude or correlation function of a quantum mechanical or statistical field theory
Structural formulasare graphical representations of molecules
Venn diagramsshows logical relations between a finite collection of sets.
Drakon-chartsare a graphical representation of algorithms and procedural knowledge.
Unified Modeling Languageis a standard notation for many types of diagrams

Other systems

Whyte notationfor classifying steam locomotives by wheel arrangement

References

^Crystal, David (2011).Dictionary of Linguistics and Phonetics.John Wiley & Sons.ISBN 9781444356755.
^"Notation".Merriam-Webster Dictionary.Encyclopædia Britannica.Retrieved6 September2013.