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# Tau (Τ, τ) Definition

Tau (Τ, τ) is the 19th letter of the Greek alphabet. In the system of Greek numerals it has a value of 300. The name in English is pronounced /taʊ/ or /tɔː/, but in modern Greek it is [taf]. This is because the pronunciation of the combination of Greek letters αυ has changed from ancient to modern times from one of [au] to either [av] or [af], depending on what follows (see Greek orthography). Tau was derived from the Phoenician letter taw. Letters that arose from tau include Roman T and Cyrillic Te (Т, т).

## Usage in Mathematics & Science

The uppercase (Τ) & lowercase (τ) Tau are used for:

• Mathematics:

• Divisor function in number theory, also denoted d or σ0

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

• Kendall tau rank correlation coefficient in statistics.

• Stopping time in stochastic processes.

• Tau, a circle constant equal to 2π (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).

• 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 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.

• Torque, the rotational force in mechanics.

• The symbol for tortuosity in hydrogeology.

• 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.

## Greek Alphabet

The letters of the Ancient Greek Alphabet, which are frequently utilized in math and science:

 Greek Alphabet Symbol Letter Symbol Letter Uppercase Lowercase Uppercase Lowercase Α α Alpha Ν ν Nu Β β Beta Ξ ξ Xi Γ γ Gamma Ο ο Omicron Δ δ Delta Π π Pi Ε ε Epsilon Ρ ρ Rho Ζ ζ Zeta Σ σ Sigma Η η Eta Τ τ Tau Θ θ Theta Υ υ Upsilon Ι ι Iota Φ φ Phi Κ κ Kappa Χ χ Chi Λ λ Lambda Ψ ψ Psi Μ μ Mu Ω ω Omega

### Sources

“Tau.” Wikipedia, Wikimedia Foundation, 6 Apr. 2020, en.wikipedia.org/wiki/Tau.

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