Rho (uppercase Ρ, lowercase ρ or ; el, ρο or el, ρω, label=none) is the 17th letter of the
Greek alphabet
The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BCE. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as we ...
. In the system of
Greek numerals
Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal numbers and in contexts similar to tho ...
it has a value of 100. It is derived from
Phoenician letter res . Its uppercase form uses the same
glyph
A glyph () is any kind of purposeful mark. In typography, a glyph is "the specific shape, design, or representation of a character". It is a particular graphical representation, in a particular typeface, of an element of written language. A g ...
, Ρ, as the distinct
Latin
Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...
letter
P; the two letters have
different Unicode encodings.
Uses
Greek
Rho is classed as a
liquid consonant
In phonetics, liquids are a class of consonants consisting of voiced lateral approximants like together with rhotics like .
Etymology
The grammarian Dionysius Thrax used the Ancient Greek word (, ) to describe the sonorant consonants () of cl ...
(together with
Lambda
Lambda (}, ''lám(b)da'') is the 11th letter of the Greek alphabet, representing the voiced alveolar lateral approximant . In the system of Greek numerals, lambda has a value of 30. Lambda is derived from the Phoenician Lamed . Lambda gave rise ...
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 a time period from the History of writing, beginning of writing and recorded human history to as far as late antiquity. The span of recorded history is roughly 5,000 years, beginning with the Sumerian language, Sumerian c ...
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 ...
, it represents a
alveolar trill
The voiced alveolar trill is a type of consonantal sound used in some spoken languages. The symbol in the International Phonetic Alphabet that represents dental, alveolar, and postalveolar trills is , and the equivalent X-SAMPA symbol is r. ...
,
alveolar tap Alveolus (; pl. alveoli, adj. alveolar) is a general anatomical term for a concave cavity or pit.
Uses in anatomy and zoology
* Pulmonary alveolus, an air sac in the lungs
** Alveolar cell or pneumocyte
** Alveolar duct
** Alveolar macrophage
* M ...
, or
alveolar approximant
The voiced alveolar approximant is a type of consonantal sound used in some spoken languages. The symbol in the International Phonetic Alphabet that represents the alveolar and postalveolar approximants is , a lowercase letter ''r'' rotated 18 ...
.
In
polytonic orthography
Greek orthography has used a variety of diacritics starting in the Hellenistic period. The more complex polytonic orthography ( el, πολυτονικό σύστημα γραφής, translit=polytonikó sýstīma grafī́s), which includes fi ...
, a rho at the beginning of a word is written with a
rough breathing
In the polytonic orthography of Ancient Greek, the rough breathing ( grc, δασὺ πνεῦμα, dasỳ pneûma or ''daseîa''; la, spīritus asper) character is a diacritical mark used to indicate the presence of an sound before a vowel, ...
, equivalent to ''h'' ( ''rh''), and a
double
A double is a look-alike or doppelgänger; one person or being that resembles another.
Double, The Double or Dubble may also refer to:
Film and television
* Double (filmmaking), someone who substitutes for the credited actor of a character
* Th ...
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 used in polytonic orthography. In Ancient Greek, it marks the absence of the voiceless glottal frica ...
over the first rho and a rough breathing over the second ( ''rrh''). That apparently reflected an
aspirated or
voiceless
In linguistics, voicelessness is the property of sounds being pronounced without the larynx vibrating. Phonologically, it is a type of phonation, which contrasts with other states of the larynx, but some object that the word phonation implies ...
pronunciation in
Ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...
, 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 (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 are also conventionally used outside the Greek alphabetical context in
science
Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe.
Science may be as old as the human species, and some of the earliest archeological evidence for ...
and
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
.
*In the
physical sciences
Physical science is a branch of natural science that studies non-living systems, in contrast to life science. It in turn has many branches, each referred to as a "physical science", together called the "physical sciences".
Definition
Phy ...
to represent:
**Densities:
mass density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
,
air density or
charge density
In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in ...
(''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
Rho (uppercase Ρ, lowercase ρ or ; el, ρο or el, ρω, label=none) is the 17th 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 sa ...
(ρ
+, ρ
−, ρ
0)
**
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 ju ...
, 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 is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
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 c ...
,
cylindrical,
spherical
A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the ce ...
, and
toroidal coordinate systems, and
toroidal and poloidal
Toroidal describes something which resembles or relates to a torus or toroid:
Mathematics
*Torus
*Toroid, a surface of revolution which resembles a torus
*Toroidal polyhedron
*Toroidal coordinates, a three-dimensional orthogonal coordinate system ...
coordinates of the Earth's magnetic field.
**The
correlation coefficient
A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables. The variables may be two columns of a given data set of observations, often called a sample, or two components ...
of a population parameter
**The
spectral radius
In mathematics, the spectral radius of a square matrix is the maximum of the absolute values of its eigenvalues. More generally, the spectral radius of a bounded linear operator is the supremum of the absolute values of the elements of its spectru ...
of a matrix
denoted as
**The
plastic number
In mathematics, the plastic number (also known as the plastic constant, the plastic ratio, the minimal Pisot number, the platin number, Siegel's number or, in French, ) is a mathematical constant which is the unique real solution of the cubic ...
**The
prime constant
The prime constant is the real number \rho whose nth binary digit is 1 if n is prime and 0 if n is composite or 1.
In other words, \rho is the number whose binary expansion corresponds to the indicator function of the set of prime numbers. Tha ...
**The
sensitivity to interest rates of a pricing function
**The expected return of a given policy (
) in
reinforcement learning
Reinforcement learning (RL) is an area of machine learning concerned with how intelligent agents ought to take actions in an environment in order to maximize the notion of cumulative reward. Reinforcement learning is one of three basic machine ...
, denoted
*In
economics
Economics () is the 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 intera ...
to represent the discount rate of future pence cash flows
*In
molecular biology
Molecular biology is the branch of biology that seeks to understand the molecular basis of biological activity in and between cells, including biomolecular synthesis, modification, mechanisms, and interactions. The study of chemical and physi ...
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 that seeks to understand the molecular basis of biological activity in and between cells, including biomolecular synthesis, modification, mechanisms, and interactions. The study of chemical and physi ...
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 foun ...
, important for cytoskeletal dynamic regulation.
*In
ecology
Ecology () is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere level. Ecology overlaps wi ...
to represent the population damping ratio where ρ = λ1 / , λ2, .
*In
computer programming
Computer programming is the process of performing a particular computation (or more generally, accomplishing a specific computing result), usually by designing and building an executable computer program. Programming involves tasks such as ana ...
**The lower-case rho "⍴" means reshape in the
APL programming language
APL (named after the book ''A Programming Language'') is a programming language developed in the 1960s by Kenneth E. Iverson. Its central datatype is the multidimensional array. It uses a large range of special graphic symbols to represent mos ...
, 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 was introduced by Edgar F. Codd.
The main application of relational algebr ...
*In
statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
to represent
Spearman's rank correlation coefficient
In statistics, Spearman's rank correlation coefficient or Spearman's ''ρ'', named after Charles Spearman and often denoted by the Greek letter \rho (rho) or as r_s, is a nonparametric measure of rank correlation ( statistical dependence betwee ...
, 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 due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, th ...
Chi Rho
The letter rho overlaid with
chi
Chi or CHI may refer to:
Greek
*Chi (letter), the Greek letter (uppercase Χ, lowercase χ);
Chinese
*Chi (length), ''Chi'' (length) (尺), a traditional unit of length, about ⅓ meter
*Chi (mythology) (螭), a dragon
*Chi (surname) (池, pin ...
forms the ''
Chi Rho'' symbol, used to represent
Jesus Christ
Jesus, likely from he, יֵשׁוּעַ, translit=Yēšūaʿ, label=Hebrew/Aramaic ( AD 30 or 33), also referred to as Jesus Christ or Jesus of Nazareth (among other names and titles), was a first-century Jewish preacher and religious ...
.
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[Unicode 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
*
P, p - Latin
References
{{Wiktionary, Ρ, ρ
Greek letters