Sigma

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Sigma (upper-case ?, lower-case ?, lower-case in word-final position ?; Greek: ?????) 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 (?) is used, e.g. ???????? (Odysseus); note the two sigmas in the center of the name, and the word-final sigma at the end.

Video Sigma

History

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

Etymology

The name of sigma, according to one hypothesis, may continue that of Phoenician Samekh. According to a different theory, its original name may have been san (the name today associated with another, obsolete letter), while sigma was a Greek innovation that simply meant "hissing", based on a nominalization of a verb ???? (síz?, from earlier *sig-j?, meaning 'I hiss').

Lunate sigma

In handwritten Greek during the Hellenistic period (4th and 3rd centuries BC), the epigraphic form of ? was simplified into a C-like shape. It is also found on coins from the fourth century BC onward. This became the universal standard form of sigma during late antiquity and the Middle Ages. It is today known as lunate sigma (upper-case ?, lower-case ?), 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. The forms of the Cyrillic letter ? (representing /s/) and Coptic letter ? sima are derived from lunate sigma.

A dotted lunate sigma (sigma periestigmenon, encoded at U+03FE ?) 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 (?), may mark a line that is out of place. A dotted antisigma or dotted reversed sigma (antisigma periestigmenon: ?) may indicate a line after which rearrangements should be made, or to variant readings of uncertain priority.

Maps 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 /?/.

African Latin alphabets

Berber

Upper-case ? may be used in the Berber Latin alphabet for [?], though the INALCO standard uses ? instead.

Uppercase of esh

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: ?).

Science and mathematics

Upper-case

Upper-case ? is used as a symbol for:

• the summation operator

  e.g.: ${\displaystyle \sum _{k=0}^{5}k=0+1+2+3+4+5=15}$

• 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 ${\displaystyle \;|\!\!\!\Sigma }$ to distinguish it from the summation operator.
• The busy beaver function

Lower-case

Lower-case ? 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 (6?), based on the standard deviation
• sigma-algebras, sigma-fields, and sigma-finiteness in measure theory; in general terms, the symbol ? serves as a shorthand for "countably", e.g. a ?-compact topological space is one that can be written as a countable union of compact subsets.
• the generated sigma-algebra of a set ${\displaystyle A}$ is denoted ${\displaystyle \sigma (A)}$
• 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 matrix ${\displaystyle A}$, denoted as ${\displaystyle \sigma (A)}$, 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
• the Weierstrass sigma-function
• the Sigmoid/Logistic function in machine learning

Groups

Politics

During the 1930s, an upper-case ? was in use as the symbol of the Ação Integralista Brasileira, a fascist political party in Brazil.

Companies

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.

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Character encodings

• Greek Sigma

• Coptic Sima

• Mathematical Sigma

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.

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See also

• Antisigma
• Greek letters used in mathematics, science, and engineering
• Sampi
• 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.

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References

Vijayan Ettickan

Source of the article : Wikipedia