Tau
Greek alphabet  



History  
Use in other languages  
Related topics  
Tau (uppercase Τ, lowercase τ; Greek: ταυ ) 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 or ,^{[1]} but in modern Greek it is . 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).
The letter occupies the Unicode slots U+03C4 (lowercase) and U+03A4 (uppercase). In HTML, they can be produced with named entities (τ
and Τ
), decimal references (τ
and Τ
), or hexadecimal references (τ
and Τ
).
Contents

Modern usage 1
 Biology 1.1
 Mathematics 1.2
 Physics 1.3
 Popular culture 1.4
 Symbolism 2
 Character Encodings 3
 References 4
Modern usage
The lowercase letter τ is used as a symbol for:
 specific tax amount.
 TAU (spacecraft), proposed spacecraft
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 (protein) in biochemistry is a protein associated with microtubules and is 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 σ_{0}
 golden ratio (1.618...), although φ (phi) is more common.^{[2]}
 Kendall tau rank correlation coefficient in statistics
 Stopping time in stochastic processes
 Tau (τ = 2π = 6.283...), the name for the ratio constant of a circle's circumference to its radius
 Taufunction in number theory
 Torsion of a curve in differential geometry
Physics
 The prefix of many stars, via the Bayer stellar designation system. (Tau Ceti is such a star)
 Proper time in relativity
 Shear stress in continuum mechanics
 The lifetime of a spontaneous emission process
 tau lepton, 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 of any device, such as an RC circuit
 Torque, the rotational force in mechanics
 The symbol for tortuosity in hydrogeology
Popular culture
 The Tau are a race in the tabletop miniature wargame Warhammer 40,000.
Symbolism
 In ancient times, Tau was used as a symbol for life and/or resurrection, whereas the eighth letter of the Greek alphabet, theta, was considered the symbol of death.
 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, IPA /t/
 The symbolism of the cross 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, a mock legal prosecution called The Consonants at Law — Sigma v. Tau in the Court of Seven Vowels contains a reference to the cross attribution. Sigma 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 named stauros after him by men
 Tau is usually considered as the symbol of Franciscan orders due to St. Francis' love for it, symbol of the redemption and of the Cross. Almost all Franciscan churches have painted a tau with two crossing arms, both with stigmata, the one of Jesus and the other of Francis; usually members of the Secular Franciscan Order wear a wooden τ in a string with three knots around the neck
Character Encodings
 Greek / Coptic Tau^{[3]}
Character  Τ  τ  Ⲧ  ⲧ  

Unicode name  GREEK CAPITAL LETTER TAU  GREEK SMALL LETTER TAU  COPTIC CAPITAL LETTER TAU  COPTIC SMALL LETTER TAU  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  932  U+03A4  964  U+03C4  11430  U+2CA6  11431  U+2CA7 
UTF8  206 164  CE A4  207 132  CF 84  226 178 166  E2 B2 A6  226 178 167  E2 B2 A7 
Numeric character reference  Τ  Τ  τ  τ  Ⲧ  Ⲧ  ⲧ  ⲧ 
Named character reference  Τ  τ  
DOS Greek  147  93  171  AB  
DOS Greek2  208  D0  238  EE  
Windows 1253  212  D4  244  F4  
TeX  \tau 
 Mathematical Tau
Character  횻  훕  훵  휏  휯  흉  

Unicode name 
MATHEMATICAL BOLD CAPITAL TAU 
MATHEMATICAL BOLD SMALL TAU 
MATHEMATICAL ITALIC CAPITAL TAU 
MATHEMATICAL ITALIC SMALL TAU 
MATHEMATICAL BOLD ITALIC CAPITAL TAU 
MATHEMATICAL BOLD ITALIC SMALL TAU 

Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  120507  U+1D6BB  120533  U+1D6D5  120565  U+1D6F5  120591  U+1D70F  120623  U+1D72F  120649  U+1D749 
UTF8  240 157 154 187  F0 9D 9A BB  240 157 155 149  F0 9D 9B 95  240 157 155 181  F0 9D 9B B5  240 157 156 143  F0 9D 9C 8F  240 157 156 175  F0 9D 9C AF  240 157 157 137  F0 9D 9D 89 
UTF16  55349 57019  D835 DEBB  55349 57045  D835 DED5  55349 57077  D835 DEF5  55349 57103  D835 DF0F  55349 57135  D835 DF2F  55349 57161  D835 DF49 
Numeric character reference  𝚻  𝚻  𝛕  𝛕  𝛵  𝛵  𝜏  𝜏  𝜯  𝜯  𝝉  𝝉 
Character  흩  힃  힣  ힽ  

Unicode name 
MATHEMATICAL SANSSERIF BOLD CAPITAL TAU 
MATHEMATICAL SANSSERIF BOLD SMALL TAU 
MATHEMATICAL SANSSERIF BOLD ITALIC CAPITAL TAU 
MATHEMATICAL SANSSERIF BOLD ITALIC SMALL TAU 

Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  120681  U+1D769  120707  U+1D783  120739  U+1D7A3  120765  U+1D7BD 
UTF8  240 157 157 169  F0 9D 9D A9  240 157 158 131  F0 9D 9E 83  240 157 158 163  F0 9D 9E A3  240 157 158 189  F0 9D 9E BD 
UTF16  55349 57193  D835 DF69  55349 57219  D835 DF83  55349 57251  D835 DFA3  55349 57277  D835 DFBD 
Numeric character reference  𝝩  𝝩  𝞃  𝞃  𝞣  𝞣  𝞽  𝞽 
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.
References
 ^
 ^ Weisstein, Eric W., "Golden Ratio", MathWorld.
 ^ Unicode Code Charts: Greek and Coptic (Range: 037003FF)