Theta (, ) uppercase Θ or '; lowercase θ or '; thē̂ta ; Modern Greek: thī́ta ) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth 𐤈. In the system of Greek numerals, it has a value of 9.
Greek
In
Ancient Greek, θ represented the aspirated voiceless dental plosive , but in
Modern Greek it represents the voiceless dental fricative .
Forms
In its archaic form, θ was written as a cross within a circle (as in the Etruscan or ), and later, as a line or point in circle ( or ).
The cursive form was retained by Unicode as , separate from . (There is also .) For the purpose of writing Greek text, the two can be font variants of a single character, but are also used as distinct symbols in technical and mathematical contexts. is also common in biblical and theological usage; e.g. () is printed .
Latin
In the Latin script used for the
Gaulish language, theta inspired the
tau gallicum (Ꟈ ꟈ). The phonetic value of the
tau gallicum is thought to have been .
In addition, multiple modern languages written in Latin script use
Latin theta.
Cyrillic
The
early Cyrillic letter
fita (Ѳ, ѳ) developed from θ. This letter existed in the
Russian alphabet until the 1918 Russian orthography reform.
International Phonetic Alphabet
In the International Phonetic Alphabet (IPA), represents the voiceless dental fricative, as in
th ick or thin.
It does not represent the consonant in
the, which is the voiced dental fricative counterpart, represented in the IPA by (cf.
Eth). A similar-looking lower-case symbol, , which is called
barred o, is the IPA symbol for the close-mid central rounded vowel.
Mathematics and science
Lower case
The lowercase letter θ is used as a symbol for:
-
A angle in geometry
-
Angle (bold) and angular separation in physics
-
An unknown angular variable in trigonometry
-
A theta function of several complex variables θ.
-
The first Chebyshev function in prime number theory
-
The potential temperature in meteorology
-
Dimensionless temperature in heat transport phenomena
-
The score of a test taker in item response theory
-
Theta Type Replication: a type of bacterial DNA replication specific to circular chromosomes
-
Threshold value of an artificial neuron
-
A Bayer designation letter applied to a star in a constellation; usually the eighth star so labelled but not necessarily the eighth-brightest as viewed from Earth
-
The statistical parameter frequently used in writing the likelihood function
-
The Watterson estimator for the population mutation rate in population genetics
-
Indicates a minimum optimum integration level determined by the intersection of GG and LL schedules (The GG-LL schedules are tools used in analyzing the potential benefits of a country pegging their domestic currency to a foreign currency.)
-
The reserve ratio of banks in economic models
-
The ordinal collapsing function developed by Solomon Feferman
-
The Heaviside step function
-
In pharmacology, the fraction of ligand bound to a macromolecule based on the Hill Equation
-
The angle of the incident beam during X-ray diffraction
Upper case
The uppercase letter Θ is used as a symbol for:
-
Theta function
-
Dimension of temperature, by SI unit (in italics)
-
An asymptotically tight bound in the analysis of algorithms (big O notation)
-
A certain ordinal number in set theory
-
, exotic in particle physics
-
A brain signal frequency (beta, alpha, theta, delta) ranging from 4–8 Hz
-
One of the variables known as "Greeks" in finance, representing time decay of options or the change in the intrinsic value of an option divided by the number of days until the option expires
Symbolism
In ancient times,
Tau was used as a symbol for
life or
resurrection, whereas the eighth letter of the Greek alphabet (ninth in the archaic form anciently used for numeration), theta, was considered the symbol of
death.
A quotation attributed to the ancient Roman author
Ennius (though possibly spuriously) said of it: "oh, theta, a letter much unluckier than the others".
According to Porphyry of Tyros, the Ancient Egypt used an X within a circle as a symbol of the soul; having a value of nine, it was used as a symbol for Ennead. Johannes Lydus says that the Egyptians used a symbol for cosmos in the form of theta, with a fiery circle representing the world, and a snake spanning the middle representing Agathos Daimon (literally: good spirit).[.]
Abbreviation
In classical Athens, it was used as an abbreviation for the
Greek language θάνατος (
Thanatos, "death") and as it vaguely resembles a human skull,
theta was used as a warning symbol of
Thanatos, in the same way that skull and crossbones are used in modern times.
It survives on
used by Athenians when voting for the
death penalty.
Petrus de Dacia in a document from 1291 relates the idea that theta was used to brand criminals as empty ciphers, and the branding rod was affixed to the crossbar spanning the circle.
[.] For this reason, the use of the number 9 was sometimes avoided where the connotation was felt to be unlucky—the mint marks of some Late Imperial Roman coins famously have the sum ΔΕ or ΕΔ (delta and epsilon, that is 4 and 5) substituted as a
euphemism where a Θ (9) would otherwise be expected.
Unicode
See also
Notes and references
Notes
