Theta (, ; uppercase: Θ or ; lowercase: θ or ; grc, ''thē̂ta'' ;

Modern Modern may refer to: History * Modern history ** Early Modern period ** Late Modern period *** 18th century *** 19th century *** 20th century ** Contemporary history * Moderns, a faction of Freemasonry that existed in the 18th century Phil ...

: ''thī́ta'' ) is the eighth letter of the

Greek alphabet The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BCE. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as we ...

, derived from the Phoenician letter Teth . In the system of

Greek numerals Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal numbers and in contexts similar to tho ...

, it has a value of 9.

Greek

Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...

, θ represented the aspirated

voiceless dental plosive The voiceless alveolar, dental and postalveolar plosives (or stops) are types of consonantal sounds used in almost all spoken languages. The symbol in the International Phonetic Alphabet that represents voiceless dental, alveolar, and postalv ...

, but in

Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the dialects of the Greek language spoken in the modern era, including the official standardized form of the ...

it represents the

voiceless dental fricative The voiceless dental non-sibilant fricative is a type of consonantal sound used in some spoken languages. It is familiar to English speakers as the 'th' in ''think''. Though rather rare as a phoneme in the world's inventory of languages, it is en ...

Forms

In its

archaic Archaic is a period of time preceding a designated classical period, or something from an older period of time that is also not found or used currently: *List of archaeological periods **Archaic Sumerian language, spoken between 31st - 26th cent ...

form, θ was written as a cross within a circle (as in the Etruscan or ), and later, as a line or point in circle ( Circled dash

or ). The cursive form was retained by

Unicode Unicode, formally The Unicode Standard,The formal version reference is is an information technology Technical standard, standard for the consistent character encoding, encoding, representation, and handling of Character (computing), text expre ...

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. Extensive lists of examples follow below at Mathematics and Science. is also common in biblical and theological usage e.g. instead of πρόθεσις (means placing in public or laying out a corpse).

Latin

In Latin script used for the

Gaulish language Gaulish was an ancient Celtic language spoken in parts of Continental Europe before and during the period of the Roman Empire. In the narrow sense, Gaulish was the language of the Celts of Gaul (now France, Luxembourg, Belgium, most of Switzer ...

, theta inspired the ''

tau gallicum Tau gallicum (majuscule:Ꟈ(), minuscule: ꟈ()) is a letter that was used to write the Gaulish language.). The phonetic value of the ''tau gallicum'' is thought to have been . Theta itself is used alongside Latin letters in Halkomelem, an indigenous North American language.

Cyrillic

The early Cyrillic letter '' fita'' (Ѳ, ѳ) developed from θ. This letter existed in the

Russian alphabet The Russian alphabet (russian: ру́сский алфави́т, russkiy alfavit, , label=none, or russian: ру́сская а́збука, russkaya azbuka, label=none, more traditionally) is the script used to write the Russian language. I ...

until the 1918 Russian orthography reform.

International Phonetic Alphabet

In the

International Phonetic Alphabet The International Phonetic Alphabet (IPA) is an alphabetic system of phonetic transcription, phonetic notation based primarily on the Latin script. It was devised by the International Phonetic Association in the late 19th century as a standa ...

(IPA), represents the

, as in ''thick'' or ''thin''. It does not represent the consonant in ''the'', which is the voiced dental fricative. A similar-looking symbol, � which is described as a lowercase barred o, indicates in the IPA a

close-mid central rounded vowel The close-mid central rounded vowel, or high-mid central rounded vowel, is a type of vowel sound. The symbol in the International Phonetic Alphabet that represents this sound is , a lowercase Ɵ, barred letter o. The character ɵ has been use ...

Mathematics and Science

Lower case

The lowercase letter θ is used as a symbol for: *A plane angle in geometry *An unknown variable in

trigonometry Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. T ...

* The

, spelled θ *A special function of several complex variables *One of the

Chebyshev function In mathematics, the Chebyshev function is either a scalarising function (Tchebycheff function) or one of two related functions. The first Chebyshev function or is given by :\vartheta(x)=\sum_ \ln p where \ln denotes the natural logarithm, w ...

s in prime number theory *The

potential temperature The potential temperature of a parcel of fluid at pressure P is the temperature that the parcel would attain if adiabatically brought to a standard reference pressure P_, usually . The potential temperature is denoted \theta and, for a gas well-a ...

meteorology Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not ...

*The score of a test taker in item response theory *Theta Type Replication: a type of bacterial

DNA replication In molecular biology, DNA replication is the biological process of producing two identical replicas of DNA from one original DNA molecule. DNA replication occurs in all living organisms acting as the most essential part for biological inheritanc ...

specific to circular

chromosomes A chromosome is a long DNA molecule with part or all of the genetic material of an organism. In most chromosomes the very long thin DNA fibers are coated with packaging proteins; in eukaryotic cells the most important of these proteins are ...

*Threshold value of an artificial neuron *A

Bayer designation A Bayer designation is a stellar designation in which a specific star is identified by a Greek or Latin letter followed by the genitive form of its parent constellation's Latin name. The original list of Bayer designations contained 1,564 stars. ...

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 In statistics, as opposed to its general use in mathematics, a parameter is any measured quantity of a statistical population that summarises or describes an aspect of the population, such as a mean or a standard deviation. If a population exa ...

frequently used in writing the

likelihood function The likelihood function (often simply called the likelihood) represents the probability of random variable realizations conditional on particular values of the statistical parameters. Thus, when evaluated on a given sample, the likelihood funct ...

*The Watterson estimator for the

population mutation rate In genetics, the mutation rate is the frequency of new mutations in a single gene or organism over time. Mutation rates are not constant and are not limited to a single type of mutation; there are many different types of mutations. Mutation rates ...

population genetics Population genetics is a subfield of genetics that deals with genetic differences within and between populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as adaptation, speciation, and pop ...

*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 In mathematical logic and set theory, an ordinal collapsing function (or projection function) is a technique for defining ( notations for) certain recursive large countable ordinals, whose principle is to give names to certain ordinals much larger ...

developed by Solomon Feferman *

Heaviside step function The Heaviside step function, or the unit step function, usually denoted by or (but sometimes , or ), is a step function, named after Oliver Heaviside (1850–1925), the value of which is zero for negative arguments and one for positive argume ...

*In

pharmacology Pharmacology is a branch of medicine, biology and pharmaceutical sciences concerned with drug or medication action, where a drug may be defined as any artificial, natural, or endogenous (from within the body) molecule which exerts a biochemica ...

, the fraction of ligand bound to a macromolecule based on the Hill Equation

Upper case

The uppercase letter Θ is used as a symbol for: *

Dimension In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), lin ...

temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...

, by SI standard (in italics) *Dimensionless temperature in transport phenomena *An asymptotically tight bound in the

analysis of algorithms In computer science, the analysis of algorithms is the process of finding the computational complexity of algorithms—the amount of time, storage, or other resources needed to execute them. Usually, this involves determining a function that re ...

(

big O notation Big ''O'' notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by Paul Bachmann, Edmund Lan ...

) *A certain

ordinal number In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, th, etc.) aimed to extend enumeration to infinite sets. A finite set can be enumerated by successively labeling each element with the least n ...

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...

* Pentaquarks, exotic

baryon In particle physics, a baryon is a type of composite subatomic particle which contains an odd number of valence quarks (at least 3). Baryons belong to the hadron family of particles; hadrons are composed of quarks. Baryons are also classified ...

s in

particle physics Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...

*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 *A variable indicating temperature difference in heat transfer *Measuring the angle of incident X-ray beam during XRD

Symbolism

Retiarius vs secutor from Borghese mosaic

In ancient times,

Tau Tau (uppercase Τ, lowercase τ, or \boldsymbol\tau; el, ταυ ) is the 19th letter of the Greek alphabet, representing the voiceless dental or alveolar plosive . In the system of Greek numerals, it has a value of 300. The name in English ...

was used as a symbol for

life Life is a quality that distinguishes matter that has biological processes, such as signaling and self-sustaining processes, from that which does not, and is defined by the capacity for growth, reaction to stimuli, metabolism, energ ...

resurrection Resurrection or anastasis is the concept of coming back to life after death. In a number of religions, a dying-and-rising god is a deity which dies and is resurrected. Reincarnation is a similar process hypothesized by other religions, which ...

, whereas the eighth letter of the Greek alphabet, theta, was considered the symbol of

death Death is the irreversible cessation of all biological functions that sustain an organism. For organisms with a brain, death can also be defined as the irreversible cessation of functioning of the whole brain, including brainstem, and brain ...

. According to

Porphyry of Tyros __NOTOC__ Porphyry (; el, Πορφύριος, links=no, ''Porphyrios'' "purple-clad") may refer to: * Porphyry (geology), an igneous rock with large crystals in a fine-grained matrix and important Roman building material * Porphyritic, the gene ...

, the

Egyptian Egyptian describes something of, from, or related to Egypt. Egyptian or Egyptians may refer to: Nations and ethnic groups * Egyptians, a national group in North Africa ** Egyptian culture, a complex and stable culture with thousands of years of ...

s used an X within a circle as a

symbol A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different conc ...

of the soul; having a value of nine, it was used as a symbol for

Ennead The Ennead or Great Ennead was a group of nine deities in Egyptian mythology worshipped at Heliopolis: the sun god Atum; his children Shu and Tefnut; their children Geb and Nut; and their children Osiris, Isis, Set, and Nephthys. The Ennead ...

Johannes Lydus John the Lydian or John Lydus ( el, ; la, Ioannes Laurentius Lydus) (ca. AD 490 – ca. 565) was a Byzantine administrator and writer on antiquarian subjects. Life and career He was born in 490 AD at Philadelphia in Lydia, whence his cognomen ...

says that the

Egyptians Egyptians ( arz, المَصرِيُون, translit=al-Maṣriyyūn, ; arz, المَصرِيِين, translit=al-Maṣriyyīn, ; cop, ⲣⲉⲙⲛ̀ⲭⲏⲙⲓ, remenkhēmi) are an ethnic group native to the Nile, Nile Valley in Egypt. Egyptian ...

used a symbol for Kosmos in the form of theta, with a fiery circle representing the world, and a snake spanning the middle representing ''

Agathos Daimon An agathodaemon ( grc, ἀγαθοδαίμων, ) or agathos daemon (, , ) was a spirit (''daemon'') of ancient Greek religion. They were personal or supernatural companion spirits, comparable to the Roman '' genii'', who ensured good luck, fert ...

'' (literally: ''good spirit'').. The Egyptians also used the symbol of a point within a circle (, the ''sun disc'') to represent the sun, which might be a possible origin of its use as the Sun's astrological glyph. It is worthwhile to note that (''theta'') has the same numerical value in isopsephy as Ηλιος (''

Helios In ancient Greek religion and Greek mythology, mythology, Helios (; grc, , , Sun; Homeric Greek: ) is the deity, god and personification of the Sun (Solar deity). His name is also Latinized as Helius, and he is often given the epithets Hyper ...

''): 318.

Abbreviation

In classical Athens, it was used as an abbreviation for the Greek θάνατος (''Thanatos'', "death") and as it vaguely resembles a human skull, theta was used as a warning symbol of

, in the same way, that skull and crossbones are used in modern times. It survives on

potsherd In archaeology, a sherd, or more precisely, potsherd, is commonly a historic or prehistoric fragment of pottery, although the term is occasionally used to refer to fragments of stone and glass vessels, as well. Occasionally, a piece of broken p ...

s used by Athenians when voting for the

death penalty Capital punishment, also known as the death penalty, is the state-sanctioned practice of deliberately killing a person as a punishment for an actual or supposed crime, usually following an authorized, rule-governed process to conclude that t ...

. 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 A euphemism () is an innocuous word or expression used in place of one that is deemed offensive or suggests something unpleasant. Some euphemisms are intended to amuse, while others use bland, inoffensive terms for concepts that the user wishes ...

where a Θ (9) would otherwise be expected. Greek Life The names of many American

fraternities and sororities Fraternities and sororities are social organizations at colleges and universities in North America. Generally, membership in a fraternity or sorority is obtained as an undergraduate student, but continues thereafter for life. Some accept gradu ...

are named with Greek letters, including Theta.

Character encodings

* Greek Theta * Coptic Thethe * Cyrillic Fita * Mathematical Theta These characters are used only as mathematical symbols. Stylized Greek text should be encoded using normal Greek letters, with markup and formatting to indicate text style.

Notes and references

Notes

References

{{Reflist Greek letters Phonetic transcription symbols