Editing Tau (section)

== Modern usage ==
{{See also|Greek letters used in mathematics, science, and engineering#Ττ (tau)}}

The lower-case letter τ is used as a symbol for:
* [[Per unit tax|Specific tax]] amount<ref>{{Cite web|url=http://faculty.maxwell.syr.edu/jomcpeak/PPA723/lecture4.htm|title=McPeak, Lecture 4|last=McPeak|first=John|date=10 Jun 2010|website=Syracuse University|archive-url=https://web.archive.org/web/20100610000249/http://faculty.maxwell.syr.edu/jomcpeak/PPA723/lecture4.htm|archive-date=10 Jun 2010|url-status=live|access-date=27 Oct 2017}}</ref>

=== Biology ===
* The expressed period of the [[Free-running sleep|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]]<ref>{{Cite journal|last1=MJ|first1=Shelton|last2=MB|first2=Wire|last3=Y|first3=Lou|last4=B|first4=Adamkiewicz|last5=SS|first5=Min|date=Mar 2016|title=Pharmacokinetic and safety evaluation of high-dose combinations of fosamprenavir and ritonavir|pmid=16495253|pmc=1426463|journal=Antimicrobial Agents and Chemotherapy|volume=50|issue=3|pages=928–934|doi=10.1128/AAC.50.3.928-934.2006}}</ref>
* The core variable in [[general tau theory]]
* [[Tau (protein)|Tau]] in biochemistry, a protein associated with [[microtubule]]s and implicated in neurodegenerative diseases such as [[Alzheimer's disease]], some forms of [[frontotemporal lobar degeneration]], and [[chronic traumatic encephalopathy]]<ref>{{Cite journal|last1=C|first1=González|last2=G|first2=Farías|last3=RB|first3=Maccioni|date=1 Nov 1998|title=Modification of tau to an Alzheimer's type protein interferes with its interaction with microtubules|journal=Cell Mol Biol (Noisy-le-grand)|volume=44 | issue = 7 |pages=1117–1127|via=EuropeMC|pmid=9846894}}</ref><ref>{{Cite journal|last1=M|first1=Sjögren|last2=E|first2=Englund|date=2004|title=Negative neurofilament light and tau immunostaining in frontotemporal dementia|pmid=15178951|journal= Dementia and Geriatric Cognitive Disorders|volume=17|issue=4|pages=346–349|doi=10.1159/000077169|s2cid=9306507}}</ref>

=== Mathematics ===
* [[Divisor function]] in number theory, also denoted ''d'' or σ<sub>0</sub><ref>{{Cite web|url=http://mathworld.wolfram.com/DivisorFunction.html|title=Divisor Function|last=Weisstein|first=Eric W.|date=27 Oct 2017|website=MathWorld --A Wolfram Web Resource.|archive-url=https://web.archive.org/web/20170629140345/http://mathworld.wolfram.com/DivisorFunction.html|archive-date=29 Jun 2017|url-status=live|access-date=28 Oct 2017}}</ref><ref group="note" name=":0">The 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.</ref>
* [[Ramanujan tau function]]<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Tau Function |url=https://mathworld.wolfram.com/TauFunction.html |access-date=2025-01-31 |website=mathworld.wolfram.com |language=en |quote=A function τ(n) related to the divisor function σ(n), also sometimes called Ramanujan's tau function.}}</ref><ref>{{Cite web |title=DLMF: §27.14 Unrestricted Partitions ‣ Additive Number Theory ‣ Chapter 27 Functions of Number Theory |url=https://dlmf.nist.gov/27.14#vi |access-date=2025-01-31 |website=dlmf.nist.gov}}</ref>
* [[Golden ratio]] (1.618...), although φ ([[phi]]) is more common<ref>{{Cite web|url=http://mathworld.wolfram.com/GoldenRatio.html|title=Golden Ratio.|last=Weisstein|first=Eric W.|date=27 Oct 2017|website=Mathworld -- A Wolfram Web Resource|archive-url=https://web.archive.org/web/20170822072337/http://mathworld.wolfram.com/GoldenRatio.html|archive-date=22 Aug 2017|url-status=live|access-date=28 Oct 2017}}</ref><ref name=":0" group="note" />
* [[Kendall tau rank correlation coefficient]] in statistics<ref>{{Cite journal|last=Ghent|first=A. W.|date=June 1963|title=Kendall's "Tau" Coefficient as an Index of Similarity in Comparisons of Plant or Animal Communities|url=https://www.cambridge.org/core/journals/canadian-entomologist/article/kendalls-tau-coefficient-as-an-index-of-similarity-in-comparisons-of-plant-or-animal-communities/B791FA0F9D0450699CF9F1AE92D5DA9D|journal=The Canadian Entomologist|volume=95| issue = 6|pages=568–575|via=Cambridge University Press|doi=10.4039/ent95568-6|s2cid=84897435 }}</ref>
* [[Stopping time]] in stochastic processes.<ref>{{Cite web|url=https://almostsure.wordpress.com/2009/11/23/sigma-algebras-at-a-stopping-time/|title=Sigma Algebras at a Stopping Time|last=Lowther|first=George|date=23 Nov 2009|website=Almost Sure at Wordpress|archive-url=https://web.archive.org/web/20161221152426/https://almostsure.wordpress.com/2009/11/23/sigma-algebras-at-a-stopping-time/|archive-date=21 Dec 2016|url-status=live|access-date=28 Oct 2017}}</ref><ref group="note" name=":1">The archived version of this source may take a few minutes to render the [[TeX]] math codes properly.</ref>
* [[Tau (mathematical constant)|Tau]], the ratio of the circumference to the radius of a circle, which is equal to 2[[pi|{{pi}}]] (6.28318...) Tau is also used to calculate how many rads are in a circle. <ref>{{Cite web|url=https://tauday.com/tau-manifesto|title=The Tau Manifesto|last=Hartl|first=Michael|author-link=Michael Hartl|date=28 Jun 2010|website=Tau Day|archive-url=https://web.archive.org/web/20171007085119/https://tauday.com/tau-manifesto|archive-date=7 Oct 2017|url-status=live|access-date=28 Oct 2017}}</ref><ref>{{Cite web|last=Bartholomew|first=Randyn Charles|date=June 25, 2014|title=Let's Use Tau--It's Easier Than Pi|url=https://www.scientificamerican.com/article/let-s-use-tau-it-s-easier-than-pi/|url-status=live|archive-url=https://web.archive.org/web/20170908232803/https://www.scientificamerican.com/article/let-s-use-tau-it-s-easier-than-pi/|archive-date=September 8, 2017|access-date=2020-08-31|website=Scientific American|language=en}}</ref>
* [[Tau function (disambiguation)|Tau function]]s, several
* [[Torsion of a curve]] in differential geometry<ref>{{Cite web|url=http://mathworld.wolfram.com/Torsion.html|title=Torsion |last=Weisstein|first=Eric W. |website=Wolfram MathWorld|archive-url=https://web.archive.org/web/20170829220240/http://mathworld.wolfram.com/Torsion.html|archive-date=29 Aug 2017|url-status=live|access-date=28 Oct 2017}}</ref><ref name=":0" group="note" />
* [[Translation (geometry)|Translation]] in Euclidean geometry (although the Latin letter [[T]] is used more often)
* The [[Prouhet–Thue–Morse constant]]<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Thue-Morse Sequence |url=https://mathworld.wolfram.com/Thue-MorseSequence.html |access-date=2025-01-31 |website=mathworld.wolfram.com |language=en |quote=The Thue-Morse sequence, also called the Morse-Thue sequence or Prouhet-Thue-Morse sequence (Allouche and Cosnard 2000), is one of a number of related sequences of numbers obtained from the parities of the counts of 1's in the binary representation of the nonnegative integers.}}</ref>

=== Physics ===
* [[Proper time]] in relativity
* [[Shear stress]] in continuum mechanics<ref>{{Citation |last=Elert |first=Glenn |title=Special Symbols |date=2023 |work=The Physics Hypertextbook|quote= τ shear stress |url=https://physics.info/symbols/ |access-date=2025-02-01 |publisher=hypertextbook |language=en}}</ref>
* The lifetime of a [[spontaneous emission]] process
* [[Tau (particle)|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]]<ref>{{Citation |last=Elert |first=Glenn |title=Special Symbols |date=2023 |work=The Physics Hypertextbook|quote= τ time constant |url=https://physics.info/symbols/ |access-date=2025-02-01 |publisher=hypertextbook |language=en}}</ref>
* [[Torque]], the rotational force in mechanics<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Tau |url=https://mathworld.wolfram.com/Tau.html |access-date=2025-02-01 |website=mathworld.wolfram.com |language=en |quote=The symbol also has a number of other different meanings in physics, for example the tau particle, tau neutrino, as a symbol for torque, etc.}}</ref><ref>{{Citation |last=Elert |first=Glenn |title=Special Symbols |date=2023 |work=The Physics Hypertextbook |quote= '''τ''', τ torque|url=https://physics.info/symbols/ |access-date=2025-02-01 |publisher=hypertextbook |language=en}}</ref>
* The symbol for [[tortuosity]] in hydrogeology
* In thermal physics, the symbol for the fundamental temperature <math>\tau = k_B T</math>