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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

Related Definitions

Sources

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

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