Theta

Theta (Template:IPAc-en, Template:IPAc-en) uppercase Θ; lowercase θ; Template:Langx thē̂ta Template:IPA; Modern: Template:Lang thī́ta Template:IPA) 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 Template:IPA, but in Modern Greek it represents the voiceless dental fricative Template:IPA.

Forms

Modern print theta, in a typical uppercase and two different lowercase glyph 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 ).

In modern print, lowercase theta may appear in two different forms: one resembling the uppercase form, like a zero with a horizontal bar through it, and one more cursive style featuring an open loop, resembling a nine. For use as a mathematical symbol, where the difference between the two forms may be significant, a dedicated Unicode symbol Template:Unichar was introduced, which always displays the open-loop form. There is also Template:Unichar, which differs from most realizations of the normal textual uppercase letter by having a cross-bar that goes all the way across, touching the outer O-shape on both sides.

Latin

The name ARAÐÐOVNA on a Gaulish tombstone

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 Template:IPA.<ref>Template:Cite web</ref> 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), Template:IPA represents the voiceless dental fricative, as in thick or thin.<ref>Template:Cite book</ref> It does not represent the consonant in the, which is the voiced dental fricative counterpart, represented in the IPA by Template:IPA (cf. Eth). A similar-looking lower-case symbol, Template:IPA, 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 plane angle in geometry<ref>Template:Cite web</ref>
• Angle (bold) and angular separation in physics<ref>Template:Citation</ref>
• An unknown angular variable in trigonometry
• A special function Template:Math of several complex variables θ.
• The first Chebyshev function Template:Math in prime number theory<ref>Template:Cite web</ref>
• The potential temperature in meteorology<ref>Template:Cite book</ref>
• Dimensionless temperature in heat transport phenomena<ref>Template:Cite book</ref>
• The score of a test taker in item response theory<ref>Template:Cite book</ref>
• 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<ref>Template:Cite book</ref>
• The statistical parameter frequently used in writing the likelihood function<ref>Template:Cite book</ref>
• The Watterson estimator Template:Mvar for the population mutation rate in population genetics<ref>Template:Cite book</ref>
• 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.)<ref>Template:Cite book</ref>
• The reserve ratio of banks in economic models<ref>Template:Cite book</ref>
• The ordinal collapsing function developed by Solomon Feferman<ref>Template:Cite journal</ref>
• The Heaviside step function<ref>Template:Cite web</ref>
• In pharmacology, the fraction of ligand bound to a macromolecule based on the Hill Equation<ref>Template:Cite book</ref>
• The angle of the incident beam during X-ray diffraction<ref>Template:Cite book</ref>

Upper case

The uppercase letter Θ is used as a symbol for:

• Theta functions<ref>Template:Cite web</ref>
• Dimension of temperature, by SI standard (in italics)<ref>Template:Cite book</ref>
• An asymptotically tight bound in the analysis of algorithms (big O notation)
• A certain ordinal number in set theory
• Pentaquarks, exotic baryons 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<ref>Template:Cite book</ref>

Symbolism

θ (θάνατος, death) in a mosaic

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.<ref name="Mednik">Template:Cite journal</ref> A quotation attributed to the ancient Roman author Ennius (though possibly spuriously) said of it: "oh, theta, a letter much unluckier than the others".<ref>Template:Cite book</ref>

According to Porphyry of Tyros, the Egyptians 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 Kosmos in the form of theta, with a fiery circle representing the world, and a snake spanning the middle representing Agathos Daimon (literally: good spirit).<ref name="Barry_1">Template:Citation.</ref>

Abbreviation

Template:Main In classical Athens, it was used as an abbreviation for the Greek θάνατος (Thanatos, "death") and as it vaguely resembles a human skull,<ref name="Barry_1"/> theta was used as a warning symbol of death, in the same way that skull and crossbones are used in modern times.<ref name="Barry_1"/> It survives on potsherds used by Athenians when voting for the death penalty.<ref name="Barry_1"/> 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.<ref>Template:Citation.</ref> 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

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See also

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