Rho (letter)

Rho (uppercase Ρ, lowercase ρ or Unicode|ϱ) is the 17th letter of the Greek alphabet. In the system of Greek numerals it has a value of 100. It is derived from Semitic Rêš "head" (see Resh). Its uppercase form is not to be confused with the Roman letter P.

Rho is generally classed as a liquid (together with lambda and sometimes the nasals mu and nu), which has important implications for morphology. It is pronounced similarly to the letter "r" in languages with a Latin-derived alphabet. In polytonic orthography a rho at the beginning of a word is conventionally written with a rough breathing (equivalent to "h") — polytonic|ῥ — and a double rho within a word is written with a smooth breathing over the first rho and a rough breathing over the second — polytonic|ῤῥ — apparently reflecting an aspirated or voiceless pronunciation in Ancient Greek, hence the various Greek-derived English words which start with "rh" or contain "rrh". The name of the letter is written in Greek as Unicode|ῥῶ (polytonic) or ρω/ρο (monotonic).

Letters that arose from rho include Roman R and Cyrillic Er (Р).

Common notational uses

The characters Ρ, ρ and Unicode|ϱ are also used outside its Greek alphabetical context in Science, and Mathematics.

*In Physics
**to represent Density (ρ)
**to represent Resistivity (ρ)

*In Mathematics
**to represent the Radius in a system of spherical polar coordinates
**to represent the correlation coefficient of a population parameter
**to represent the Spectral radius of a matrix $A$ denoted as $ho(A)$
**to represent a Plastic number

*In Economics to represent the discount rate of future pence cash flows

*In Molecular Biology to represent the Rho protein responsible for termination of RNA synthesis. In such occasions, it is often represented as unicode|ϱ ("rho symbol" U+03F1), to avoid confusion with the Latin letter "p"

*In Programming
**For LaTeX, the symbols are P (Ρ), ho ($ho$), and varrho ($varrho$)
**The lower-case rho "ρ" has a special meaning in the APL programming language

See also

*Р, р - Er (Cyrillic)
*П, п - Pe (Cyrillic)
*R, r - Latin
*P, p - Latin