rho

File:NAMA Alphabet grec.jpg vessel, with an R-shaped 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|el|r|IPA}}, alveolar tap {{IPA|el|ɾ|IPA}}, or alveolar approximant {{IPA|el|ɹ|IPA}}.

In polytonic orthography, a rho at the beginning of a word is almost always written ⟨{{lang|grc|ῥ}}⟩ (rh) with a rough breathing mark, indicating that it is voiceless. Very rarely, it is written ⟨{{lang|grc|ῤ}}⟩ (r) with a smooth breathing mark, indicating that it is voiced, instead. Rho is not written with breathing marks at any other place in a word, where it is always voiced, with the exception of double rho, which was traditionally written ⟨{{lang|grc|ῤῥ}}⟩ (rrh), with a smooth breathing mark over the first rho, and a rough breathing mark over the second, representing a geminated voiceless consonant. However, this practice fell out of use over the 19th century in favour of ⟨{{lang|grc|ρρ}}⟩, since double rho cannot take any other combination of breathing marks. Various Greek-derived English words containing rh and rrh derive from words containing ⟨{{lang|grc|ῤ}}⟩ and ⟨{{lang|grc|ρρ}}⟩.

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

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

The characters ρ and {{not a typo|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.{{Citation |last=Elert |first=Glenn |title=Special Symbols |date=2023 |work=The Physics Hypertextbook |url=https://physics.info/symbols/ |access-date=2025-02-01 |publisher=hypertextbook |language=en}}
• The correlation coefficient of a population parameter
• The spectral radius of a matrix $A$ denoted as $\backslash rho(A)${{Cite web |last=Weisstein |first=Eric W. |title=Spectral Radius |url=https://mathworld.wolfram.com/SpectralRadius.html |access-date=2025-01-22 |website=mathworld.wolfram.com |language=en}}
• The plastic ratio{{Cite web |last=Weisstein |first=Eric W. |title=Plastic Constant |url=https://mathworld.wolfram.com/PlasticConstant.html |access-date=2025-01-31 |website=mathworld.wolfram.com |language=en |quote=The plastic constant ρ, sometimes also called le nombre radiant, the minimal Pisot number, plastic number, plastic ratio,...}}
• The prime constant{{Cite web |last=Weisstein |first=Eric W. |title=Prime Constant |url=https://mathworld.wolfram.com/PrimeConstant.html |access-date=2025-01-31 |website=mathworld.wolfram.com |language=en}}
• The sensitivity to interest rates of a pricing function
• The expected return of a given policy ($\backslash pi$) in reinforcement learning, denoted $\backslash rho^\backslash pi$
• The rename operation in relational algebra
• In economics to represent the discount rate of future cash flows{{Citation needed|date=January 2025}}
• In molecular biology to represent the Rho protein responsible for termination of RNA synthesis. In such occasions, it is often represented as {{unichar|03f1|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{{Cite web |last=Weisstein |first=Eric W. |title=Spearman Rank Correlation Coefficient |url=https://mathworld.wolfram.com/SpearmanRankCorrelationCoefficient.html |access-date=2025-01-22 |website=mathworld.wolfram.com |language=en |quote=The Spearman rank correlation coefficient, also known as Spearman's rho,}}
• In options theory to represent the rate of change of a portfolio with respect to interest rates{{Cite web |title=What Is Rho? Definition, How It's Used, Calculation, and Example |url=https://www.investopedia.com/terms/r/rho.asp |access-date=2025-01-22 |website=Investopedia |language=en |quote=Rho is the rate at which the price of a derivative changes relative to a change in the risk-free rate of interest. Rho measures the sensitivity of an option or options portfolio to a change in interest rate.}}

File:Simple Labarum2.svg symbol representing Christ.]]

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 {{lang|el|γϼ}} for {{lang|el|γράμμα}} as a unit of measurement.Paul of Aegina explains conventional usage in the last chapter of Book VII on weights and measures and uses it throughout his work.

• {{unichar|03A1|html=}}Unicode Code Charts: [https://www.unicode.org/charts/PDF/U0370.pdf Greek and Coptic (Range: 0370-03FF)]
• {{unichar|03C1|html=}}
• {{unichar|03F1|html=}}
• {{unichar|03FC}}
• {{unichar|1D29}}
• {{unichar|1D68}}
• {{unichar|1FE4}}
• {{unichar|1FE5}}
• {{unichar|1FEC}}
• {{unichar|2374}}
• {{unichar|2627}}
• {{unichar|2CA2}}
• {{unichar|2CA3}}
• {{unichar|2CE5}}
• {{unichar|2CE6}}
• {{unichar|2CE8}}
• {{unichar|2CE9}}
• {{unichar|101A0}}

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:

• {{unichar|1D6B8}}
• {{unichar|1D6D2}}
• {{unichar|1D6E0}}
• {{unichar|1D6F2}}
• {{unichar|1D70C}}
• {{unichar|1D71A}}
• {{unichar|1D72C}}
• {{unichar|1D746}}
• {{unichar|1D754}}
• {{unichar|1D766}}
• {{unichar|1D780}}
• {{unichar|1D78E}}
• {{unichar|1D7A0}}
• {{unichar|1D7BA}}
• {{unichar|1D7C8}}

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

{{Wiktionary|Ρ|ρ}}

Category:Greek letters