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Tau (uppercase Τ, lowercase τ, or \boldsymbol\tau; el, ταυ ) is the 19th letter of the
Greek alphabet The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BCE. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as ...
, representing the voiceless dental or alveolar plosive . In the system of
Greek numerals Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal numbers and in contexts similar to those ...
, it has a value of 300. The name in English is pronounced or , but in
Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...
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 The orthography of the Greek language ultimately has its roots in the adoption of the Greek alphabet in the 9th century BC. Some time prior to that, one early form of Greek, Mycenaean, was written in Linear B, although there was a lapse of several ...
). Tau was derived from the Phoenician letter taw (𐤕). Letters that arose from tau include Roman T and Cyrillic Te (Т, т). The letter occupies the
Unicode Unicode, formally The Unicode Standard,The formal version reference is is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, ...
slots U+03C4 (lowercase) and U+03A4 (uppercase). In
HTML The HyperText Markup Language or HTML is the standard markup language for documents designed to be displayed in a web browser. It can be assisted by technologies such as Cascading Style Sheets (CSS) and scripting languages such as JavaS ...
, they can be produced with named entities (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 A per unit tax, or specific tax, is a tax that is defined as a fixed amount for each unit of a good or service sold, such as cents per kilogram. It is thus proportional to the particular quantity of a product sold, regardless of its price. Excise t ...
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 1 ...
s and implicated in neurodegenerative diseases such as
Alzheimer's disease Alzheimer's disease (AD) is a 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 remembering recent events. As ...
, some forms of frontotemporal lobar degeneration, and
chronic traumatic encephalopathy Chronic traumatic encephalopathy (CTE) is a neurodegenerative disease linked to repeated trauma to the head. The encephalopathy symptoms can include behavioral problems, mood problems, and problems with thinking. The disease often gets worse ...


Mathematics

*
Divisor function In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as ''the'' divisor function, it counts the ''number of divisors of an integer'' (includin ...
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 In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0, where the Greek letter phi ( ...
(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 probability theory, in particular in the study of stochastic processes, a stopping time (also Markov time, Markov moment, optional stopping time or optional time ) is a specific type of “random time”: a random variable whose value is inter ...
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 the differential geometry of curves in three dimensions, the torsion of a curve measures how sharply it is twisting out of the osculating plane. Taken together, the curvature and the torsion of a space curve are analogous to the curvature of ...
in differential geometry *
Translation Translation is the communication of the meaning of a source-language text by means of an equivalent target-language text. The English language draws a terminological distinction (which does not exist in every language) between ''transla ...
in Euclidean geometry (although the Latin letter T is used more often) * The
Prouhet–Thue–Morse constant In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in mode ...


Physics

*
Proper time In relativity, proper time (from Latin, meaning ''own time'') along a timelike world line is defined as the time as measured by a clock following that line. It is thus independent of coordinates, and is a Lorentz scalar. The proper time interval ...
in relativity *
Shear stress Shear stress, often denoted by ( Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. '' Normal stress'', on ...
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 ...
process * Tau, an elementary particle in particle physics * Tau in
astronomy Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...
is a measure of
optical depth In physics, optical depth or optical thickness is the natural logarithm of the ratio of incident to ''transmitted'' radiant power through a material. Thus, the larger the optical depth, the smaller the amount of transmitted radiant power throug ...
, or how much sunlight cannot penetrate the atmosphere * In the physical sciences, tau is sometimes used as
time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...
variable, to avoid confusing t as temperature *
Time constant In physics and engineering, the time constant, usually denoted by the Greek letter (tau), is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system.Concretely, a first-order LTI system is a s ...
(also
relaxation time In the physical sciences, relaxation usually means the return of a perturbed system into equilibrium. Each relaxation process can be categorized by a relaxation time τ. The simplest theoretical description of relaxation as function of 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 ...
*
Torque In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of th ...
, the rotational force in mechanics * The symbol for
tortuosity Tortuosity is widely used as a critical parameter to predict transport properties of porous media, such as rocks and soils. But unlike other standard microstructural properties, the concept of tortuosity is vague with multiple definitions and vari ...
in hydrogeology


Symbolism

* In ancient times, tau was used as a symbol for
life Life is a quality that distinguishes matter that has biological processes, such as signaling and self-sustaining processes, from that which does not, and is defined by the capacity for growth, reaction to stimuli, metabolism, energy ...
or
resurrection Resurrection or anastasis is the concept of coming back to life after death. In a number of religions, a dying-and-rising god is a deity which dies and is resurrected. Reincarnation is a similar process hypothesized by other religions, whic ...
, whereas the eighth letter of the Greek alphabet,
theta Theta (, ; uppercase: Θ or ; lowercase: θ or ; grc, ''thē̂ta'' ; Modern: ''thī́ta'' ) 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. G ...
, was considered the symbol of
death Death is the irreversible cessation of all biological functions that sustain an organism. For organisms with a brain, death can also be defined as the irreversible cessation of functioning of the whole brain, including brainstem, and brain ...
. * In Biblical times, the taw 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 The voiceless alveolar, dental and postalveolar plosives (or stops) are types of consonantal sounds used in almost all spoken languages. The symbol in the International Phonetic Alphabet that represents voiceless dental, alveolar, and posta ...
, IPA /t/ * The symbolism of the
cross A cross is a geometrical figure consisting of two intersecting lines or bars, usually perpendicular to each other. The lines usually run vertically and horizontally. A cross of oblique lines, in the shape of the Latin letter X, is termed a s ...
was connected not only to the letter chi 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 who is best known for his characteristic tongue-in-cheek style, with which he frequently ridiculed supersti ...
, a mock legal prosecution called '' The Consonants at Law - Sigma vs. Tau, in the Court of the Seven Vowels'', 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 a ...
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 A gibbet is any instrument of public execution (including guillotine, executioner's block, impalement stake, hanging gallows, or related scaffold). Gibbeting is the use of a gallows-type structure from which the dead or dying bodies of cri ...
named ''stauros'' after him by men'' * Tau is usually considered as the symbol of
Franciscan , image = FrancescoCoA PioM.svg , image_size = 200px , caption = A cross, Christ's arm and Saint Francis's arm, a universal symbol of the Franciscans , abbreviation = OFM , predecessor = , ...
orders due to St. Francis' love for it, symbol of the redemption and of the
Cross A cross is a geometrical figure consisting of two intersecting lines or bars, usually perpendicular to each other. The lines usually run vertically and horizontally. A cross of oblique lines, in the shape of the Latin letter X, is termed a s ...
. Almost all Franciscan churches have painted a tau with two crossing arms, both with
stigmata Stigmata ( grc, στίγματα, plural of , 'mark, spot, brand'), in Roman Catholicism, are bodily wounds, scars and pain which appear in locations corresponding to the crucifixion wounds of Jesus Christ: the hands, wrists, and feet. Sti ...
, the one of Jesus and the other of Francis; members of the
Secular Franciscan Order The Secular Franciscan Order ( la, Ordo Franciscanus Saecularis; abbreviated OFS) is the third branch of the Franciscan Family formed by Catholic men and women who seek to observe the Gospel of Jesus by following the example of Francis of Assisi ...
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