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Rho (uppercase Ρ, lowercase ρ or ; el, ῥῶ) is the 17th letter of the
Greek alphabet The Greek alphabet has been used to write the Greek language since the late ninth or early eighth century BC. It is derived from the earlier Phoenician alphabet, and was the first alphabetic script in history to have distinct letters for vowels ...

Greek alphabet
. In the system of
Greek numerals Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a numeral system, system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal number (linguistics), ordi ...
it has a value of 100. It is derived from
Phoenician letter
Phoenician letter
res
res
. Its uppercase form uses the same
glyph The term glyph is used in typography Typography is the art and technique of arranging type to make written language A written language is the representation of a spoken or gestural language A language is a structured system o ...
, Ρ, as the distinct
Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of the Roman Republic, it became ...

Latin
letter
P
P
; the two letters have different Unicode encodings.


Uses


Greek

Rho is classed as a
liquid consonant In phonetics Phonetics is a branch of that studies how humans produce and perceive sounds, or in the case of s, the equivalent aspects of sign. Phoneticians—linguists who specialize in phonetics—study the physical properties of speech. Th ...
(together with
Lambda Lambda (; uppercase , lowercase ; el, λάμ(β)δα, ''lám(b)da'') is the 11th letter of the Greek alphabet, representing the sound Dental, alveolar and postalveolar lateral approximants, /l/. In the system of Greek numerals, lambda has a ...
and sometimes the nasals Mu and Nu), which has important implications for
morphology Morphology, from the Greek and meaning "study of shape", may refer to: Disciplines * Morphology (archaeology), study of the shapes or forms of artifacts * Morphology (astronomy), study of the shape of astronomical objects such as nebulae, galaxies ...
. In both
Ancient Ancient history is the aggregate of past eventsWordNet Search – 3.0
"History"
from ...
and
Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the dialects of the Greek language spoken in the modern era, including the official standardized form of the l ...
, it represents a trilled or
tapped r
tapped r
. In
polytonic orthography Greek orthographyThe orthography of the Greek language ultimately has its roots in the adoption of the Greek alphabet in the 9th century BC. Some time prior to that, one early form of Greek, Mycenaean language, Mycenaean, was written in Linear ...
, a rho at the beginning of a word is written with a
rough breathing In the polytonic orthography Greek orthographyThe orthography of the Greek language ultimately has its roots in the adoption of the Greek alphabet in the 9th century BC. Some time prior to that, one early form of Greek, Mycenaean language, My ...
, equivalent to ''h'' ( ''rh''), and a
double Double may refer to: * Look-alike, a person who closely resembles another person * Double (filmmaking), someone who substitutes for the credited actor of a character * Doppelgänger, ghostly double of a living person * Polish Enigma doubles, repl ...

double
rho within a word is written with a
smooth breathing The smooth breathing ( grc, ψιλὸν πνεῦμα, psilòn pneûma; ell, ψιλή ''psilí''; la, spīritus lēnis) is a diacritical mark A diacritic (also diacritical mark, diacritical point, diacritical sign, or accent) is a glyph adde ...
over the first rho and a rough breathing over the second ( ''rrh''). That apparently reflected an aspirated or
voiceless In linguistics Linguistics is the science, scientific study of language. It encompasses the analysis of every aspect of language, as well as the methods for studying and modeling them. The traditional areas of linguistic analysis include ...

voiceless
pronunciation in
Ancient Greek Ancient Greek includes the forms of the Greek language Greek ( el, label=Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the diale ...
, 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 (polytonic) or ρω/ ρο (monotonic).


Other alphabets

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


Mathematics and science

The characters ρ and are also conventionally used outside the Greek alphabetical context in
science Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is something that is truth, true. The usual test for a statement of ...

science
and
mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ...
. *In the
physical sciences Physical science is a branch of natural science Natural science is a branch A branch ( or , ) or tree branch (sometimes referred to in botany Botany, also called , plant biology or phytology, is the science of plant life and a b ...
to represent: **Densities:
mass density The density (more precisely, the volumetric mass density; also known as specific mass), of a substance is its mass per unit volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter Rho (letter), rho), although the L ...
,
air density The density of air or atmospheric density, denoted ''ρ'' (Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Sout ...
or
charge density In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is c ...

charge density
(''ρ'') **
Resistivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
(''ρ'') **
Rho meson In particle physics Particle physics (also known as high energy physics) is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department ...
+, ρ, ρ0) ** General quantum states **
Hammett Equation The Hammett equation in organic chemistry describes a linear free-energy relationship relating reaction rates and equilibrium constants for many reactions involving benzoic acid derivatives with meta- and para- substituents to each other with ...
, 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 Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ...
to represent: **A length coordinate in
polar Polar may refer to: Geography Polar may refer to: * Geographical pole, either of two fixed points on the surface of a rotating body or planet, at 90 degrees from the equator, based on the axis around which a body rotates *Polar climate, the clim ...

polar
,
cylindrical A cylinder (from ) has traditionally been a Solid geometry, three-dimensional solid, one of the most basic of curvilinear geometric shapes. Geometrically, it can be considered as a Prism (geometry), prism with a circle as its base. This traditi ...

cylindrical
,
spherical of a sphere A sphere (from Greek language, Greek —, "globe, ball") is a geometrical object in three-dimensional space Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values ...

spherical
, and toroidal coordinate systems, and
toroidal and poloidal Image:Toroidal coord.png, 250px, A diagram depicting the poloidal (\theta) direction, represented by the red arrow, and the toroidal (\zeta or \phi) direction, represented by the blue arrow.The terms toroidal and poloidal refer to directions relativ ...
coordinates of the Earth's magnetic field. **The
correlation coefficient A correlation coefficient is a numerical measure of some type of correlation and dependence, correlation, meaning a statistical relationship between two variable (mathematics), variables. The variables may be two column (database), columns of a give ...
of a population parameter **The
spectral radius ''Spectral'' is a 2016 American military science fiction action film Action film is a film genre in which the protagonist or protagonists are thrust into a series of events that typically include violence, extended fighting, physical feats, ...

spectral radius
of a matrix A denoted as \rho(A) **The
plastic number In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ...
**The prime constant **The sensitivity to interest rates of a pricing function **The expected return of a given policy (\pi) in
reinforcement learning Reinforcement learning (RL) is an area of machine learning Machine learning (ML) is the study of computer algorithms that can improve automatically through experience and by the use of data. It is seen as a part of artificial intelligence. M ...
, denoted \rho^\pi *In
economics Economics () is a social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interact ...

economics
to represent the discount rate of future pence cash flows *In
molecular biology Molecular biology is the branch of biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interactions, P ...
to represent the Rho protein responsible for termination of RNA synthesis. In such occasions, it is often represented as , to avoid confusion with the Latin letter ''p'' *In
molecular biology Molecular biology is the branch of biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interactions, P ...
to represent the
Rho family of GTPases The Rho family of GTPases is a family of small (~21 kDa) signaling G proteins, and is a subfamily of the Ras superfamily. The members of the Rho GTPase family have been shown to regulate many aspects of intracellular actin dynamics, and are found ...
, important for cytoskeletal dynamic regulation. *In
ecology Ecology (from el, οἶκος, "house" and el, -λογία, label=none, "study of") is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms In biol ...
to represent the population damping ratio where ρ = λ1 / , λ2, . *In
computer programming Computer programming is the process of designing and building an executable computer program to accomplish a specific computing result or to perform a particular task. Programming involves tasks such as analysis, generating algorithms, Profilin ...
**The lower-case rho "⍴" means reshape in the
APL programming language APL (named after the book ''A Programming Language'') is a programming language A programming language is a formal language comprising a Instruction set architecture, set of instructions that produce various kinds of Input/output, output. Pr ...
, and by extension also queries shape **The lower-case rho "ρ" is used for the unary rename operation in
relational algebra In database theory, relational algebra is a theory that uses algebraic structures with a well-founded semantics for modeling data, and defining queries on it. The theory has been introduced by Edgar F. Codd. The main application of relational ...
*In
statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more technical sens ...

statistics
to represent
Spearman's rank correlation coefficient 300px, When the data are roughly elliptically distributed and there are no prominent outliers, the Spearman correlation and Pearson correlation give similar values. In statistics Statistics is the discipline that concerns the collection, orga ...
, commonly known as Spearman's rho *In options theory to represent the rate of change of a portfolio with respect to
interest rates An interest rate is the amount of interest In finance Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of money and inves ...


Chi Rho

The letter rho overlaid with
chiThe initialism CHI may refer to: Health *Catholic Health Initiatives Catholic Health Initiatives (CHI) is a national Catholic healthcare system, with headquarters in Englewood, Colorado. CHI is a nonprofit, faith-based health system formed, in 19 ...
forms the ''
Chi Rho The Chi Rho (; also known as ''chrismon'') is one of the earliest forms of christogram, formed by superimposing the first two (capital) letters—chi (letter), chi and rho (ΧΡ)—of the Greek word (Christ (title), Christos) in such a way th ...

Chi Rho
'' symbol, used to represent
Jesus Christ Jesus, likely from he, יֵשׁוּעַ, translit=Yēšūaʿ, label=Hebrew Hebrew (, , or ) is a Northwest Semitic languages, Northwest Semitic language of the Afroasiatic languages, Afroasiatic language family. Historically, it i ...

Jesus Christ
.


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 rhoUnicode Code Charts
Greek and Coptic (Range: 0370-03FF)
/ref>


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
R, r - Latin
*
P, p - Latin
P, p - Latin


References

{{Wiktionary, Ρ, ρ Greek letters