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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 is pronounced or , but in Greek it is . This is because the pronunciation of the combination of Greek letters αυ can have the pronounciation of either , or , depending on what follows and if a diaeresis is present on the second vowel (see Greek orthography). Tau was derived from the Phoenician letter
taw Taw, tav, or taf is the twenty-second and last letter of the Semitic abjads, including Phoenician Tāw , Hebrew Tav , Aramaic Taw , Syriac Taw ܬ, and Arabic ت Tāʼ (22nd in abjadi order, 3rd in modern order). In Arabic, it is also gives ri ...
(𐤕). Letters that arose from tau include Roman T and Cyrillic Te (Т, т). The letter occupies the Unicode slots U+03C4 (lowercase) and U+03A4 (uppercase). In HTML, they can be produced with
named entities Named-entity recognition (NER) (also known as (named) entity identification, entity chunking, and entity extraction) is a subtask of information extraction that seeks to locate and classify named entities mentioned in unstructured text into pre ...
(τ and Τ), decimal references (τ and Τ), or hexadecimal references (τ and Τ).


Modern usage

The lower-case letter τ is used as a symbol for: * Specific tax amount


Biology

* The expressed period of the freerunning rhythm of an animal, i.e., the length of the daily cycle of an animal when kept in constant light or constant darkness * The dose interval in
pharmacokinetics Pharmacokinetics (from Ancient Greek ''pharmakon'' "drug" and ''kinetikos'' "moving, putting in motion"; see chemical kinetics), sometimes abbreviated as PK, is a branch of pharmacology dedicated to determining the fate of substances administered ...
* The core variable in
general tau theory General tau theory deals with the guidance of bodily movements. It was developed from work on J. J. Gibson's notion of ecological invariants in the visual flow-field during a perception-in-action event, and subsequently generalised by David N. Lee ...
* Tau in biochemistry, a protein associated with
microtubule Microtubules are polymers of tubulin that form part of the cytoskeleton and provide structure and shape to eukaryotic cells. Microtubules can be as long as 50 micrometres, as wide as 23 to 27  nm and have an inner diameter between 11 an ...
s and implicated in neurodegenerative diseases such as
Alzheimer's disease Alzheimer's disease (AD) is a neurodegeneration, neurodegenerative disease that usually starts slowly and progressively worsens. It is the cause of 60–70% of cases of dementia. The most common early symptom is difficulty in short-term me ...
, some forms of frontotemporal lobar degeneration, and chronic traumatic encephalopathy


Mathematics

* Divisor function in number theory, also denoted ''d'' or σ0The date given on the source is after that of the archive. This is because the original publishing date is unknown, so the latest update date is stated instead. * Golden ratio (1.618...), although φ ( phi) is more common *
Kendall tau rank correlation coefficient In statistics, the Kendall rank correlation coefficient, commonly referred to as Kendall's τ coefficient (after the Greek letter τ, tau), is a statistic used to measure the ordinal association between two measured quantities. A τ test is a n ...
in statistics * Stopping time in stochastic processes.The archived version of this source may take a few minutes to render the TeX math codes properly. * Tau, the ratio of the circumference to the radius of a circle, which is equal to 2 (6.28318...) * Tau functions, several * Torsion of a curve in differential geometry * Translation in Euclidean geometry (although the Latin letter T is used more often) * The Prouhet–Thue–Morse constant


Physics

* Proper time in relativity * Shear stress in continuum mechanics * The lifetime of a
spontaneous emission Spontaneous emission is the process in which a quantum mechanical system (such as a molecule, an atom or a subatomic particle) transits from an excited energy state to a lower energy state (e.g., its ground state) and emits a quantized amount of ...
process * Tau, an elementary particle in particle physics * Tau in astronomy is a measure of optical depth, or how much sunlight cannot penetrate the atmosphere * In the physical sciences, tau is sometimes used as time variable, to avoid confusing t as temperature * Time constant (also relaxation time) of any system, such as an
RC circuit A resistor–capacitor circuit (RC circuit), or RC filter or RC network, is an electric circuit composed of resistors and capacitors. It may be driven by a voltage or current source and these will produce different responses. A first order RC ci ...
* Torque, the rotational force in mechanics * The symbol for tortuosity in hydrogeology


Symbolism

* In ancient times, tau was used as a symbol for life or resurrection, whereas the eighth letter of the Greek alphabet, theta, was considered the symbol of death. * In Biblical times, the
taw Taw, tav, or taf is the twenty-second and last letter of the Semitic abjads, including Phoenician Tāw , Hebrew Tav , Aramaic Taw , Syriac Taw ܬ, and Arabic ت Tāʼ (22nd in abjadi order, 3rd in modern order). In Arabic, it is also gives ri ...
was put on men to distinguish those who lamented sin, although newer versions of the Bible have replaced the ancient term ''taw'' with ''mark'' (Ezekiel 9:4) or ''signature'' (Job 31:35). Its original sound value is a voiceless alveolar plosive, IPA /t/ * The symbolism of the cross was connected not only to the letter
chi Chi or CHI may refer to: Greek *Chi (letter), the Greek letter (uppercase Χ, lowercase χ); Chinese *Chi (length), ''Chi'' (length) (尺), a traditional unit of length, about ⅓ meter *Chi (mythology) (螭), a dragon *Chi (surname) (池, pin ...
but also to tau, the equivalent of the last letter in the Phoenician and Old Hebrew alphabets, and which was originally cruciform in shape; see Cross of Tau. * An essay written around 160 AD, attributed to
Lucian Lucian of Samosata, '; la, Lucianus Samosatensis ( 125 – after 180) was a Hellenized Syrian satirist, rhetorician and pamphleteer Pamphleteer is a historical term for someone who creates or distributes pamphlets, unbound (and therefore ...
, a mock legal prosecution called ''
The Consonants at Law - Sigma vs. Tau, in the Court of the Seven Vowels ''The Consonants at Law - Sigma vs. Tau, in the Court of the Seven Vowels'' is an essay attributed to Lucian, and appearing in the Loeb Classical Library edition of the Works of Lucian. However the edition notes that it is "probably not by Lucian, ...
'', contains a reference to the cross attribution.
Sigma Sigma (; uppercase Σ, lowercase σ, lowercase in word-final position ς; grc-gre, σίγμα) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase Σ is used as ...
petitions the court to sentence Tau to death by crucifixion, saying: *: ''Men weep, and bewail their lot, and curse Cadmus with many curses for introducing ''Tau'' into the family of letters; they say it was his body that tyrants took for a model, his shape that they imitated, when they set up structures on which men are crucified. ''Stauros'' (cross) the vile engine is called, and it derives its vile name from him. Now, with all these crimes upon him, does he not deserve death, nay, many deaths? For my part I know none bad enough but that supplied by his own shape — that shape which he gave to the gibbet named ''stauros'' after him by men'' * Tau is usually considered as the symbol of Franciscan orders due to St. Francis' love for it, symbol of the redemption and of the Cross. Almost all Franciscan churches have painted a tau with two crossing arms, both with stigmata, the one of Jesus and the other of Francis; members of the Secular Franciscan Order usually wear a wooden τ in a string with three knots around the neck * The title and symbol of "Tau" is used by
neo-Gnostic Gnosticism in modern times includes a variety of contemporary religious movements, stemming from Gnostic ideas and systems from ancient Roman society. Gnosticism is an ancient name for a variety of religious ideas and systems, originating in Jewis ...
bishops as it has some symbolism in many of the modern branches of Gnosticism.


Character encodings

For the Greek and Coptic letter tau: For the mathematical letter tau: 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

* Greek letters used in mathematics, science, and engineering


Notes


References

{{Authority control Greek letters Cross symbols