### Sigma (letter)

Look up , Σ, or σ in , the free dictionary.ς |

**Sigma** (upper case **Σ**, lower case **σ**, lower case in word-final position **ς**; Greek σίγμα) is the eighteenth letter of the Greek alphabet, and carries the 's' sound. In the system of Greek numerals it has a value of 200. When used at the end of a word, and the word is not all upper case, 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

## History

The shape and alphabetic position of Sigma is derived from .

### Etymology

The name of sigma, according to one hypothesis,^{[1]} may continue that of Phoenician Samekh. According to a different theory,^{[2]} 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 σίζω (*sízō*, from earlier **sig-jō*, meaning 'I hiss').

### Uppercase of esh

The uppercase form of sigma was re-borrowed into the Latin alphabet to serve as the uppercase of modern esh (lowercase: ʃ).

### Lunate sigma

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

A dotted lunate sigma (*sigma periestigmenon*, encoded at U+03FE Ͼ) was used by Aristarchus of Samothrace 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.

## Uses

### Greek

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

### Berber

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

### Science and mathematics

#### Upper case

Upper case Σ is used as a symbol for:

- the summation operator
- 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 $|\backslash !\backslash !\backslash !\backslash Sigma$ to distinguish it from the summation operator.

#### Lower case

Lower case σ is used for:

- sigma bonds in chemistry
- to represent an unknown angle in mathematics
- Velocity dispersion in astronomy
- Sigma constant in science
- the sigma receptor in biology
- the standard deviation of a population or probability distribution in statistics
- a quality model for business, Six Sigma, based on the standard deviation, often referred to as "
**6σ**" - sigma-algebras, sigma-fields and sigma-finiteness in measure theory; more generally, 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 $\backslash sigma(A)$
- 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 $A$, denoted as $\backslash sigma(A)$, 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 (EW)
- 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.
^{[5]}

### Politics

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

## Companies

Sigma Corporation uses the name of the letter but not the letter itself, however in many internet forums photographers refer to the company or its lenses using the sigma letter.

## Character encodings

- Greek Sigma

^{[6]}

- 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.

## See also

- Antisigma
- Greek letters used in mathematics, science, and engineering
- Sampi
- Sibilant consonant
- ∑, or summation
- Theta Sigma
- "Sigm-" as a combining form, as in
*sigm*odon,*sigm*urethra, or in the derivative "sigmoid", as in sigmoid sinus, sigmoid colon, sigmoidoscopy, etc.