Theta

Look up Θ or θ in Wiktionary, the free dictionary.

Greek alphabet
Αα	Alpha	Νν	Nu
Ββ	Beta	Ξξ	Xi
Γγ	Gamma	Οο	Omicron
Δδ	Delta	Ππ	Pi
Εε	Epsilon	Ρρ	Rho
Ζζ	Zeta	Σσς	Sigma
Ηη	Eta	Ττ	Tau
Θθ	Theta	Υυ	Upsilon
Ιι	Iota	Φφ	Phi
Κκ	Kappa	Χχ	Chi
Λλ	Lambda	Ψψ	Psi
Μμ	Mu	Ωω	Omega
History
Archaic local variants
Ligatures (ϛ, ȣ, ϗ) Diacritics
Numerals ϛ (6) ϟ (90) ϡ (900)
In other languages
Bactrian Coptic Albanian
Scientific symbols
Book Category Commons view talk edit

Theta (uppercase Θ, lowercase θ or ϑ;^[1] Ancient Greek θῆτα [tʰɛ̂ːta]; Modern Greek θήτα [ˈθita]; UK /ˈθiːtə/, US /ˈθeɪtə/) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth . In the system of Greek numerals it has a value of 9.

Greek

The alphabet on a black figure vessel, with a point-and-circle theta.

In Ancient Greek, θ represented the aspirated voiceless dental plosive /t̪ʰ/, but in Modern Greek it represents the voiceless dental fricative /θ/.

Forms

In its archaic form, θ was written as a cross within a circle ( or ), and later, as a line or point within a circle ( or ).

Latin

The name ARAÐÐOVNA on a Gaulish tombstone.

In the Latin script used for the Gaulish language, theta developed into the tau gallicum, conventionally transliterated as Ð, although the bar extends across the centre of the letter. The phonetic value of the tau gallicum is thought to have been [t͡s].

Cyrillic

The early Cyrillic letter fita (Ѳ, ѳ) developed from θ.

International Phonetic Alphabet

In the International Phonetic Alphabet, [θ] represents the voiceless dental fricative, as in thick or thin. It does not represent the consonant in the, which is the voiced dental fricative.

Math and science

Lower case

The lower-case letter θ is used as a symbol for:

• A plane angle in geometry.
• A special function of several complex variables.
• One of the Chebyshev functions in prime number theory.
• The potential temperature in meteorology.
• 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 parameter frequently used in writing the likelihood function (Bayes theorem).
• 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 a tool 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.

Upper case

The upper-case letter Θ is used as a symbol for:

• Dimensionless temperature in transport phenomena.
• Big O notation. Denoting an asymptotically tight bound in analysis of algorithms.
• Θ (set theory), a certain ordinal number.
• Representing pentaquarks, exotic baryons in particle physics.
• Brain Signal Frequency (Beta, Alpha, Theta, Delta) ranging from 4–8 Hz.
• One of the variables known as "Greeks" in finance, representing the lost-value rate of an option over time.
• As a variable indicating Temperature difference in Heat Transfer

In its archaic form

• In its archaic form () theta is used as a symbol for Earth.

Greek mathematics

The common usage of theta in mathematical problems began with the Greeks. They logically chose this Greek symbol since it was the next in their alphabet not yet used and was easily legible when recreating for multiple uses.

Archaic crossed forms of theta are seen in the wheel letters of Linear A, Linear B, and Egyptian hieroglyphics, the mathematical tensor product, exclusive disjunction, and direct sum operators, the identification symbol for the Earth (as already mentioned), and the Celtic cross. The circumpunct, or circled dot, is seen in a wide range of places.

Symbolism

θ (θάνατος, death) in an mosaic

• In ancient times, Tau was used as a symbol for life and/or resurrection, whereas the eighth letter of the Greek alphabet, theta, was considered the symbol of death.

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).^[2]

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 θῆτα (theta) has the same numerical value in isopsephy as Ηλιος (Helios): 318.

In modern times, L. Ron Hubbard's teachings of Scientology have expanded on the concept of a soul, or thetan (derived from the Greek letter "theta").

Abbreviation

In classical Athens, it was used as an abbreviation for the Greek θάνατος (thanatos, “death”) and as it vaguely resembles a human skull,^{[citation needed]} theta was used as a warning symbol of death, in the same way that skull and crossbones are used in modern times. It survives on potsherds used by Athenians when voting for the death penalty.^[2] 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.^[3] For this reason, use of the number theta 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.

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 the normal Greek letters, with markup and formatting to indicate text style.

See also

• Ѳ, ѳ - Fita, a letter of the early Cyrillic alphabet derived from the Greek theta
• ʘ - Bilabial click
• Voiceless dental fricative

Notes