Tau

Tau ( ; uppercase Τ, lowercase τ or τ; Greek: ταυ [taf]) is the nineteenth letter of the Greek alphabet, representing the voiceless dental or alveolar plosive IPA: [t]. In the system of Greek numerals, it has a value of 300.

The name in English is pronounced or , and in Greek it is [taf]. This is because the pronunciation of the combination of Greek letters αυ can have the pronunciation of either [ai], [av] or [af], depending on what follows and if a diaeresis is present on the second vowel or an accent mark is present on the first vowel in Greek orthography.

Tau was derived from the Phoenician letter taw (𐤕). Letters that arose from tau include Latin T and Cyrillic Te (Т, т).

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

The core variable in general tau theory

Tau in biochemistry, a protein associated with microtubules and implicated in neurodegenerative diseases such as Alzheimer's disease, some forms of frontotemporal lobar degeneration, and chronic traumatic encephalopathy

Mathematics

Divisor function in number theory, also denoted d or σ0

Ramanujan tau function

Golden ratio (1.618...), although φ (phi) is more common

Kendall tau rank correlation coefficient in statistics

Stopping time in stochastic processes.

Tau, the ratio of the circumference to the radius of a circle, which is equal to 2×π (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 process

Tau, an elementary particle in particle physics

Tau in astronomy is a measure of optical depth, or how much stellar radiation (e.g. sunlight) cannot penetrate a region

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

Torque, the rotational force in mechanics

The symbol for tortuosity in hydrogeology

In thermal physics, the symbol for the characteristic energy τ = kT

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.