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 an alveolar trill IPA: [r], alveolar tap IPA: [ɾ], or alveolar approximant IPA: [ɹ].

Inpolytonic 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 aspiratedorvoiceless pronunciation in Ancient Greek, which led to the various Greek-derived English words starting with rh or containing 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 densityorcharge 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.
• Inmathematics 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 ratio
  • 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 ${\displaystyle \rho ^{\pi }}$ 
  • The rename operation in relational algebra
• Ineconomics to represent the discount rate of future pence cash flows
• Inmolecular biology to represent the Rho protein responsible for termination of RNA synthesis. In such occasions, it is often represented as U+03F1 ϱ GREEK RHO SYMBOL, to avoid confusion with the Latin letter p
• Inmolecular biology to represent the Rho family of GTPases, important for cytoskeletal dynamic regulation.
• Inecology to represent the population damping ratio where ρ = λ1 / |λ2|.
• Incomputer programming
  • 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 operationinrelational algebra
• Instatistics to represent Spearman's rank correlation coefficient, commonly known as Spearman's rho
• Inoptions 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. It was first used by Emperor Constantine the Great. A can be seen on his standard known as the Labarum.

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.

• Р, р - Er (Cyrillic)
• R, r - Latin
• P, p - Latin