Theta

In Ancient Greek, θ originally represented the aspirated voiceless dental plosive , but it later became a voiceless dental fricative , which is the value it retains in Modern Greek. ==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 was introduced, which always displays the open-loop form. There is also , 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==

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 thigh (), thick (), enthuse (), thing (), think (), thin (), thang (), myth (), smith (), youth (), bath (), math (), birth (), fourth (), death (), or health (). 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 plane angle in geometry • Angle (bold) and angular separation in physics • An unknown angular variable in trigonometry • A special 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 functions • Dimension of temperature, by SI standard (in italics) • 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 ==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 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). Abbreviation In classical Athens, it was used as an abbreviation for the Greek θάνατος (Thanatos, "death") and as it vaguely resembles a human skull, 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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