Rho

Rho (; uppercase Ρ, lowercase ρ or ϱ; Greek: ρο or ρω) is the seventeenth 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 uses the same glyph, Ρ, as the distinct Latin letter P; the two letters have different Unicode encodings.

Uses

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

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 containing 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).

Mathematics and science

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 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
• 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 U+03F1 ϱ GREEK RHO SYMBOL, 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
  • 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

Chi Rho (☧)

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.

Rho with stroke (ϼ)

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.

Character encodings

Greek rho

Greek rho symbols

Coptic ro

Functional symbol

Mathematical rho

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.

See also

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

References

1. Chi Rho
2. Rhos
3. Del in cylindrical and spherical coordinates
4. Rho (disambiguation)
5. Rho, Lombardy
6. Electrical resistivity and conductivity
7. Relative density
8. Rho factor
9. Rho family of GTPases
10. Rho(D) immune globulin
11. Sigma Gamma Rho
12. Staurogram
13. Navier–Stokes equations
14. Bernoulli's principle
15. Sigma Rho
16. Rho meson
17. Rho Cassiopeiae
18. Terminal velocity
19. Rho Ophiuchi cloud complex
20. Cylindrical coordinate system