Rho

Rho (uppercase Ρ, lowercase ρ or ) is the 17th letter of the Greek alphabet. In the system of Greek numerals, it has a value of 100. It is derived from Phoenician letter res. Its uppercase form is not to be confused with the Latin letter P, although both are typeset using the same glyph.

Greek
Rho is classed as a liquid consonant (together with lambda and sometimes the nasals mu and nu), which has important implications for morphology. In both Ancient and Modern Greek, it represents a trilled or tapped r.

In polytonic orthography a rho at the beginning of a word is written with a rough breathing (equivalent to h) — ῥ rh — and a double rho within a word is written with a smooth breathing over the first rho and a rough breathing over the second — ῤῥ rrh — 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 ῥῶ (polytonic) or ρω/ρο (monotonic).

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

Math and science
The characters Ρ, ρ and  are also used outside its Greek alphabetical context in science and mathematics.


 * In physics to represent:
 * Densities: mass density, or charge density (ρ)
 * Resistivity (ρ)
 * Rho meson (ρ+, ρ-, ρ0)
 * General quantum states


 * In mathematics to represent:
 * The radius in the cylindrical or spherical coordinate systems
 * The correlation coefficient of a population parameter
 * The spectral radius of a matrix $$A$$ denoted as $$\rho(A)$$
 * The plastic number
 * The sensitivity to interest rates of a pricing function
 * The expected return of a given policy ($$\pi$$) in reinforcement learning, denoted $$\rho^\pi$$


 * 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 ("rho symbol" U+03F1), to avoid confusion with the Latin letter p


 * In ecology to represent the population damping ratio where ρ = λ1 / |λ2|.


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


 * In statistics to represent Spearman's rank correlation coefficient, commonly known as Spearman's rho


 * In options theory to represent the rate of change of a portfolio with respect to interest rates

Chi Rho
The letter rho overlaid with chi forms the Chi Rho symbol, used to represent Jesus Christ.

Rhodes Scholars
Former Rhodes Scholars are entitled to use the Greek letter rho as a designation of their status. When used, the symbol should precede the name.