Theta

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Θθ Theta
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'''Theta''' (uppercase '''Θ''', lowercase '''θ''' or '''ϑ''';<sup>[]</sup> [[Ancient Greek]] θῆτα tʰɛ̂ːta; [[Modern Greek]] θήτα ˈθita; ˈθiːtə, 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.
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Tabernai
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==Greek==
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Tabitha
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In [[Ancient Greek]], θ represented the [[aspiration (phonetics)|aspirated]] [[voiceless dental plosive]] /t̪ʰ/, but in [[Modern Greek]] it represents the [[voiceless dental fricative]] /θ/.
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tagma
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===Forms===
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In its [[Archaic period in Greece|archaic]] form, θ was written as:
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*a cross within a circle ([[Image:Earth symbol.svg|16px|A symbol of a cross within a circle]] or [[Image:Cross within circle 2.svg|16px|Another symbol of a cross within a circle]])
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*and later, as a line or point within a circle ([[File:Line within circle.svg|16px|The symbol of a line within a circle]] or [[Image:Sun symbol.svg|16px|The symbol of a point within a circle]]).
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==Cyrillic==
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The early [[Cyrillic]] letter ''[[fita]]'' (Ѳ, ѳ) developed from θ.
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==International Phonetic Alphabet==
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In the [[International Phonetic Alphabet]], [θ] represents the [[voiceless dental fricative]], as in '''''th'''ick'' or '''''th'''in''. It does not represent the consonant in '''''th'''e'', which is the [[voiced dental fricative]].
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==Math and science==
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===Lower case===
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The lower-case letter θ is used as a symbol for:
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*A [[angle|plane angle]] in geometry.
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*A [[theta function|special function]] of several complex variables.
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*One of the [[Chebyshev function]]s in prime number theory.
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*The [[potential temperature]] in [[meteorology]].
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*The score of a test taker in [[item response theory]].
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*Theta Type Replication: a type of bacterial [[DNA replication]] specific to circular [[chromosomes]].
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*Threshold value of an artificial neuron.
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*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.
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*The parameter frequently used in writing the [[likelihood function]] (Bayes theorem).
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*Along with μ (Mu), population parameters in the Normal/Gaussian/Bell curve distribution, usually designated N(μ,θ).
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*The [[Watterson estimator]] for the [[population mutation rate]] in [[population genetics]].
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===Upper case===
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The upper-case letter Θ is used as a symbol for:
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*Dimensionless temperature in [[transport phenomena]].
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*[[Big O notation]]. Denoting an asymptotically tight bound in analysis of algorithms.
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*[[Θ (set theory)]], a certain [[ordinal number]].
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*Representing [[pentaquark]]s, exotic [[baryon]]s in [[particle physics]].
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*[[Earth Day]].
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*[[Electroencephalography|Brain Signal Frequency]] (Beta, Alpha, Theta, Delta) ranging from 4–8&nbsp;Hz.
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*One of the variables known as [[Greeks (finance)|"Greeks"]] in finance, representing the lost-value rate of an option over time.
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*As a variable indicating Temperature difference in Heat Transfer
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===Greek mathematics===
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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.
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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.
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==Symbolism==
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According to [[Porphyry of Tyros]], the [[Ancient Egypt|Egyptian]]s 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|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'').<sup>[]</sup>
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The Egyptians also used the symbol of a point within a circle ([[Image:Sun symbol.svg|15px|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 {{Polytonic|θῆτα}} (''theta'') has the same numerical value in [[isopsephy]] as Ηλιος (''[[Helios]]''): 318.
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===Abbreviation===
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In classical Athens, it was used as an abbreviation for the [[Greek language|Greek]] θάνατος (''thanatos'', “death”) and as it vaguely resembles a human skull, theta was used as a warning symbol of [[Thanatos|death]], in the same way that [[skull and crossbones (poison)|skull and crossbones]] are used in modern times. It survives on [[potsherd]]s used by Athenians when voting for the [[death penalty]].<sup>[]</sup> [[Petrus de Dacia (mathematician)|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.<sup>[]</sup> 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.
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==Culture==
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In the science fiction TV series Doctor Who, the character of the Doctor was once known as Theta Sigma whilst he lived on Gallifrey.
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==Notes==
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==See also==
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*[[Ѳ, ѳ - Fita]], a letter of the [[early Cyrillic alphabet]] derived from the Greek theta
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*[[ʘ|ʘ - Bilabial click]]
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[[Category:Greek letters]]
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[[Category:Phonetic transcription symbols]]

Revision as of 13:32, 7 March 2011

Theta (uppercase Θ, lowercase θ or ϑ;[] Ancient Greek θῆτα tʰɛ̂ːta; Modern Greek θήτα ˈθita; ˈθiːtə, 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.

Contents

Greek

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:

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:

Upper case

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

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

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).[]

The Egyptians also used the symbol of a point within a circle (Image:Sun symbol.svg, 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): 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 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.[] 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, 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.

Culture

In the science fiction TV series Doctor Who, the character of the Doctor was once known as Theta Sigma whilst he lived on Gallifrey.

Notes

See also

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