Rho

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). That apparently reflected an aspirated or voiceless pronunciation in Ancient Greek, which led to the various Greek-derived English words starting with rh or contain rrh.

The name of the letter is written in Greek as ῥῶ (polytonic) or ρω/ρο (monotonic).

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

The characters ρ and ϱ are also conventionally used outside the Greek alphabetical context in science and mathematics.

• In the physical sciences to represent:
  • Densities: mass density, air density or charge density (ρ)
  • Resistivity (ρ)
  • Rho meson (ρ⁺, ρ⁻, ρ⁰)
  • General quantum states
  • Hammett Equation, ρ is used to represent the reaction constant, this is independent of the position and nature of the substituents of the benzene ring.
• In mathematics to represent:
  • A length coordinate in polar, cylindrical, spherical, and toroidal coordinate systems, and toroidal and poloidal coordinates of the Earth's magnetic field.
  • The correlation coefficient of a population parameter
  • The spectral radius of a matrix ${\displaystyle A}$ denoted as ${\displaystyle \rho (A)}$
  • The plastic number
  • The prime constant
  • The sensitivity to interest rates of a pricing function
  • The expected return of a given policy (${\displaystyle \pi }$) in reinforcement learning, denoted ${\displaystyle \rho ^{\pi }}$
• 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 ϱ ("rho symbol" U+03F1), to avoid confusion with the Latin letter p
• In molecular biology to represent the Rho family of GTPases, important for cytoskeletal dynamic regulation.
• In ecology to represent the population damping ratio where ρ = λ1 / |λ2|.
• In computer programming
  • For LaTeX, the symbols are \rho (${\displaystyle \rho }$), and \varrho (${\displaystyle \varrho }$) (note: \Rho is not defined by default)
  • The lower-case rho "⍴" means reshape in the APL programming language, and by extension also queries shape
  • The lower-case rho "ρ" is used for the unary rename operation in relational algebra
• 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

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

The rho with a stroke through its tail is used for abbreviations involving rho, most notably in γϼ for γράμμα as a unit of measurement.[1]

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.