Sigma
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Sigma
Sigma (uppercase Σ, lowercase σ, lowercase in word-final position ς; Greek: σίγμα) is the eighteenth letter of the Greek alphabet. In the system of Greek

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For other uses, see Sigma (disambiguation). Greek alphabet Αα Alpha Νν Nu Ββ Beta Ξξ Xi Γγ Gamma Οο Omicron Δδ Delta Ππ Pi Εε Epsilon Ρρ Rho Ζζ Zeta Σσς Sigma Ηη Eta Ττ Tau Θθ Theta Υυ Upsilon Ιι Iota Φφ Phi Κκ Kappa Χχ Chi Λλ Lambda Ψψ Psi Μμ Mu Ωω Omega History Archaic local variants
  • Diacritics
  • Ligatures
Numerals
  • ϛ (6)
  • ϟ (90)
  • ϡ (900)
Use in other languages
  • Bactrian
  • Coptic
  • Albanian
Related topics
  • Use as scientific symbols
  • Book
  • Category
  • Commons
  • v
  • t
  • e

Sigma (uppercase Σ, lowercase σ, lowercase in word-final position ς; Greek: σίγμα) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. When used at the end of a word (when the word is not all caps), the final form (ς) is used, e.g. Ὀδυσσεύς (Odysseus); note the two sigmas in the center of the name, and the word-final sigma at the end.

Contents
  • 1 History
    • 1.1 Etymology
    • 1.2 Lunate sigma
    • 1.3 Derived alphabets
  • 2 Uses
    • 2.1 Greek
    • 2.2 International African Alphabet
    • 2.3 Science and mathematics
      • 2.3.1 Uppercase
      • 2.3.2 Lowercase
    • 2.4 Organizations
  • 3 Character encoding
  • 4 See also
  • 5 References
History

The shape and alphabetic position of sigma is derived from Phoenician shin 𐤔 .

Etymology

The original name of the letter "sigma" may have been san, but due to the complicated early history of the Greek epichoric alphabets, "san" came to be identified as a separate letter, Ϻ.[1] Herodotus reports that "san" was the name given by the Dorians to the same letter called "sigma" by the Ionians.[2]

The name of sigma, according to one hypothesis,[3] may continue that of Phoenician Samekh, the letter continued by Greek Ξ. Alternatively, the name sigma may have been a Greek innovation that simply meant "hissing", from the root of σίζω (sízō, earlier *sig-jō, meaning "I hiss").[1]

Lunate sigma The Madaba Map, a sixth-century mosaic of Jerusalem (Η ΑΓΙΑ ΠΟΛΙϹ) uses the lunate sigma A plaque reading "Metochion of Gethsemanes" (Μετόχιον Γεθσημανῆς) in Jerusalem, with a lunate sigma both at the end and in the middle of the word

In handwritten Greek during the Hellenistic period (4th and 3rd centuries BC), the epigraphic form of Σ was simplified into a C-like shape.[4] It is also found on coins from the fourth century BC onward.[5] This became the universal standard form of sigma during late antiquity and the Middle Ages. It is today known as lunate sigma (uppercase Ϲ, lowercase ϲ), because of its crescent-like shape.

It is still widely used in decorative typefaces in Greece, especially in religious and church contexts, as well as in some modern print editions of classical Greek texts.

A dotted lunate sigma (sigma periestigmenon, encoded at U+03FE Ͼ) was used by Aristarchus of Samothrace (220–143 BC) as an editorial sign indicating that the line so marked is at an incorrect position. Similarly, an antisigma, or reversed sigma (Ͻ), may mark a line that is out of place. A dotted antisigma or dotted reversed sigma (antisigma periestigmenon: Ͽ) may indicate a line after which rearrangements should be made, or to variant readings of uncertain priority.

Derived alphabets

Sigma was adopted in the Old Italic alphabets beginning in the 8th century BC. A simplified three-stroke version, omitting the lowermost stroke, is found already in Western Greek alphabets, and becomes current in classical Etruscan, in Oscan, and also in the earliest Latin epigraphy (early Latin S), such as the Duenos inscription. The alternation between three and four strokes (occasionally also more than four) is also adopted into the early runic alphabet (early form of the s-rune. Both the Anglo-Saxon runes and the Younger Futhark consistently use the simplified three-stroke version.

The forms of the Coptic letter .mw-parser-output .script-coptic{font-family:"New Athena Unicode","MPH 2B Damase","FreeSerif","Arial Coptic",Quivira,Analecta,Antinoou,"Sophia Nubian","Noto Sans Coptic","Segoe UI Historic","Segoe UI Symbol"}Ⲥ sima (2nd century BC) and of Cyrillic letter С (9th century) are derived from lunate sigma.

Uses Greek

In both Ancient and Modern Greek, the sigma represents the voiceless alveolar fricative /s/. In Modern Greek, this sound is voiced to /z/ before /m/, /n/, /v/, /ð/ or /ɣ/.

International African Alphabet

The uppercase form of sigma was re-borrowed into the Latin alphabet – more precisely, the International African Alphabet – to serve as the uppercase of modern esh (lowercase: ʃ).

Science and mathematics Uppercase

Uppercase Σ is used as a symbol for:

  • the summation operator
    e.g.: ∑ k = 0 5 k = 0 + 1 + 2 + 3 + 4 + 5 = 15 {\displaystyle \sum _{k=0}^{5}k=0+1+2+3+4+5=15}
  • Sigma is the addition version of factorial.
  • a class of baryons in particle physics
  • macroscopic cross sections in nuclear and particle physics
  • self-energy in condensed matter physics
  • the balance of the invoice classes and the overall amount of the debts and demands in economics
  • the set of symbols that form an alphabet in linguistics and computer science
  • the covariance matrix of a set of random variables in probability theory and statistics, sometimes in the form | Σ {\displaystyle \;|\!\!\!\Sigma } to distinguish it from the summation operator.
  • The busy beaver function
Lowercase

Lowercase σ is used for:

  • the standard deviation of a population or probability distribution in statistics
  • sigma bonds in chemistry
  • to represent an unknown angle in mathematics
  • cross section (physics)
  • velocity dispersion in astronomy
  • sigma constant in organic chemistry
  • the sigma receptor in biology
  • a quality model for business, Six Sigma (6σ), based on the standard deviation
  • sigma-algebras, sigma-fields, and sigma-finiteness in measure theory; in general terms, the symbol σ serves as a shorthand for "countably", e.g. a σ-compact topological space is one that can be written as a countable union of compact subsets.
  • the generated sigma-algebra of a set A is denoted σ(A)
  • the sum-of-divisors function in number theory
  • the Stefan–Boltzmann constant
  • the "sigma factor" of RNA polymerase
  • a measure of electrical conductivity
  • the surface charge density in electrostatics
  • normal stress in continuum mechanics
  • volatility of a stock generally needed for options pricing
  • a syllable in phonology
  • the spectrum of a linear map T, denoted as σ(T), in applied mathematics
  • surface tension
  • the unary operation of selection on a database relation in relational algebra
  • the Pauli matrices in quantum mechanics
  • a target's radar cross-section (RCS) in radar jamming or electronic warfare
  • the life span of a basic multicellular unit (BMU) in bone remodeling
  • the damping parameter in signal processing
  • a millisecond in early 20th-century physiology literature[6]
  • the Weierstrass sigma-function
  • the Sigmoid/Logistic function in machine learning
  • the elasticity of substitution between two inputs in macroeconomics
Organizations

During the 1930s, an uppercase Σ was in use as the symbol of the Ação Integralista Brasileira, a fascist political party in Brazil.

Sigma Corporation uses the name of the letter but not the letter itself, but in many Internet forums, photographers refer to the company or its lenses using the letter. Sigma Aldrich incorporate both the name and the character in their logo.

Character encoding
Greek Sigma
Character Σ σ ς Ϲ ϲ Unicode name GREEK CAPITAL LETTER SIGMA GREEK SMALL LETTER SIGMA GREEK SMALL LETTER FINAL SIGMA GREEK CAPITAL LUNATE SIGMA SYMBOL GREEK LUNATE SIGMA SYMBOL Encodings decimal hex decimal hex decimal hex decimal hex decimal hex Unicode 931 U+03A3 963 U+03C3 962 U+03C2 1017 U+03F9 1010 U+03F2 UTF-8 206 163 CE A3 207 131 CF 83 207 130 CF 82 207 185 CF B9 207 178 CF B2 Numeric character reference Σ Σ σ σ ς ς Ϲ Ϲ ϲ ϲ Named character reference Σ σ ς DOS Greek 145 91 169 A9 170 AA DOS Greek-2 207 CF 236 EC 237 ED Windows 1253 211 D3 243 F3 242 F2 TeX \Sigma \sigma \varsigma

[7]

Character Ͻ ͻ Ͼ ͼ Ͽ ͽ Unicode name GREEK CAPITAL REVERSED LUNATE SIGMA SYMBOL GREEK SMALL REVERSED LUNATE SIGMA SYMBOL GREEK CAPITAL DOTTED LUNATE SIGMA SYMBOL GREEK SMALL DOTTED LUNATE SIGMA SYMBOL GREEK CAPITAL REVERSED DOTTED LUNATE SIGMA SYMBOL GREEK SMALL REVERSED DOTTED LUNATE SIGMA SYMBOL Encodings decimal hex decimal hex decimal hex decimal hex decimal hex decimal hex Unicode 1021 U+03FD 891 U+037B 1022 U+03FE 892 U+037C 1023 U+03FF 893 U+037D UTF-8 207 189 CF BD 205 187 CD BB 207 190 CF BE 205 188 CD BC 207 191 CF BF 205 189 CD BD Numeric character reference Ͻ Ͻ ͻ ͻ Ͼ Ͼ ͼ ͼ Ͽ Ͽ ͽ ͽ
Coptic Sima
Character Ⲥ ⲥ Unicode name COPTIC CAPITAL LETTER SIMA COPTIC SMALL LETTER SIMA Encodings decimal hex decimal hex Unicode 11428 U+2CA4 11429 U+2CA5 UTF-8 226 178 164 E2 B2 A4 226 178 165 E2 B2 A5 Numeric character reference Ⲥ Ⲥ ⲥ ⲥ
Mathematical Sigma
Character ∑ 𝚺 𝛔 𝛓 𝛴 𝜎 Unicode name N-ARY SUMMATION MATHEMATICAL BOLD
CAPITAL SIGMA MATHEMATICAL BOLD
SMALL SIGMA MATHEMATICAL BOLD
SMALL FINAL SIGMA MATHEMATICAL ITALIC
CAPITAL SIGMA MATHEMATICAL ITALIC
SMALL SIGMA Encodings decimal hex decimal hex decimal hex decimal hex decimal hex decimal hex Unicode 8721 U+2211 120506 U+1D6BA 120532 U+1D6D4 120531 U+1D6D3 120564 U+1D6F4 120590 U+1D70E UTF-8 226 136 145 E2 88 91 240 157 154 186 F0 9D 9A BA 240 157 155 148 F0 9D 9B 94 240 157 155 147 F0 9D 9B 93 240 157 155 180 F0 9D 9B B4 240 157 156 142 F0 9D 9C 8E UTF-16 8721 2211 55349 57018 D835 DEBA 55349 57044 D835 DED4 55349 57043 D835 DED3 55349 57076 D835 DEF4 55349 57102 D835 DF0E Numeric character reference ∑ ∑ 𝚺 𝚺 𝛔 𝛔 𝛓 𝛓 𝛴 𝛴 𝜎 𝜎 Named character reference ∑ Character 𝜍 𝜮 𝝈 𝝇 𝝨 Unicode name MATHEMATICAL ITALIC
SMALL FINAL SIGMA MATHEMATICAL BOLD ITALIC
CAPITAL SIGMA MATHEMATICAL BOLD ITALIC
SMALL SIGMA MATHEMATICAL BOLD ITALIC
SMALL FINAL SIGMA MATHEMATICAL SANS-SERIF
BOLD CAPITAL SIGMA Encodings decimal hex decimal hex decimal hex decimal hex decimal hex Unicode 120589 U+1D70D 120622 U+1D72E 120648 U+1D748 120647 U+1D747 120680 U+1D768 UTF-8 240 157 156 141 F0 9D 9C 8D 240 157 156 174 F0 9D 9C AE 240 157 157 136 F0 9D 9D 88 240 157 157 135 F0 9D 9D 87 240 157 157 168 F0 9D 9D A8 UTF-16 55349 57101 D835 DF0D 55349 57134 D835 DF2E 55349 57160 D835 DF48 55349 57159 D835 DF47 55349 57192 D835 DF68 Numeric character reference 𝜍 𝜍 𝜮 𝜮 𝝈 𝝈 𝝇 𝝇 𝝨 𝝨 Character 𝞂 𝞁 𝞢 𝞼 𝞻 Unicode name MATHEMATICAL SANS-SERIF
BOLD SMALL SIGMA MATHEMATICAL SANS-SERIF
BOLD SMALL FINAL SIGMA MATHEMATICAL SANS-SERIF
BOLD ITALIC CAPITAL SIGMA MATHEMATICAL SANS-SERIF
BOLD ITALIC SMALL SIGMA MATHEMATICAL SANS-SERIF
BOLD ITALIC SMALL FINAL SIGMA Encodings decimal hex decimal hex decimal hex decimal hex decimal hex Unicode 120706 U+1D782 120705 U+1D781 120738 U+1D7A2 120764 U+1D7BC 120763 U+1D7BB UTF-8 240 157 158 130 F0 9D 9E 82 240 157 158 129 F0 9D 9E 81 240 157 158 162 F0 9D 9E A2 240 157 158 188 F0 9D 9E BC 240 157 158 187 F0 9D 9E BB UTF-16 55349 57218 D835 DF82 55349 57217 D835 DF81 55349 57250 D835 DFA2 55349 57276 D835 DFBC 55349 57275 D835 DFBB Numeric character reference 𝞂 𝞂 𝞁 𝞁 𝞢 𝞢 𝞼 𝞼 𝞻 𝞻

These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.

See also Wikimedia Commons has media related to the letter sigma. Look up Σ, σ, or ς in Wiktionary, the free dictionary.
  • Antisigma
  • Greek letters used in mathematics, science, and engineering
  • Sampi
  • Sho (letter)
  • Stigma (letter)
  • Sibilant consonant
  • ∑, or summation
  • "Sigm-" as a combining form, as in sigmodon, sigmurethra, or in the derivative "sigmoid", as in sigmoid sinus, sigmoid colon, sigmoidoscopy, etc.
References
  1. ^ a b Woodard, Roger D. (2006). "Alphabet". In Wilson, Nigel Guy (ed.). Encyclopedia of ancient Greece. London: Routldedge. p. 38..mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}
  2. ^ "…τὠυτὸ γράμμα, τὸ Δωριέες μὲν σὰν καλέουσι ,Ἴωνες δὲ σίγμα" ('…the same letter, which the Dorians call "san", but the Ionians "sigma"…'; Herodotus, Histories 1.139); cf. Nick Nicholas, Non-Attic letters Archived 2012-06-28 at Archive.today.
  3. ^ Jeffery, Lilian H. (1961). The local scripts of archaic Greece. Oxford: Clarendon. pp. 25–27.
  4. ^ Edward M. Thompson (1912), Introduction to Greek and Latin paleography, Oxford: Clarendon. p. 108, 144
  5. ^ Parthia.com: Numismatica Font Projects.
  6. ^ Hill, A. V. (1935). "Units and Symbols". Nature. 136 (3432): 222. doi:10.1038/136222a0.
  7. ^ Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)


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