Rho
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Rho /ˈroʊ/ (uppercase Ρ, lowercase ρ or ϱ; Greek: ῥῶ) 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 same glyph, Ρ, as the distinct Latin letter P; the two letters have different Unicode encodings.
Uses
![](http://upload.wikimedia.org/wikipedia/commons/thumb/d/df/NAMA_Alphabet_grec.jpg/220px-NAMA_Alphabet_grec.jpg)
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 a trilled or tapped r.
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 contain 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 denoted as
- The plastic number
- The prime constant
- The sensitivity to interest rates of a pricing function
- The expected return of a given policy () in reinforcement learning, denoted
- 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.
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.[1]
Character encodings
Greek rho[2]
Preview | Ρ | ρ | Ῥ | ῥ | ῤ | |||||
---|---|---|---|---|---|---|---|---|---|---|
Unicode name | GREEK CAPITAL LETTER RHO | GREEK SMALL LETTER RHO | GREEK CAPITAL LETTER RHO WITH DASIA | GREEK SMALL LETTER RHO WITH DASIA | GREEK SMALL LETTER RHO WITH PSILI | |||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex | dec | hex |
Unicode | 929 | U+03A1 | 961 | U+03C1 | 8172 | U+1FEC | 8165 | U+1FE5 | 8164 | U+1FE4 |
UTF-8 | 206 161 | CE A1 | 207 129 | CF 81 | 225 191 172 | E1 BF AC | 225 191 165 | E1 BF A5 | 225 191 164 | E1 BF A4 |
Numeric character reference | Ρ |
Ρ |
ρ |
ρ |
Ῥ |
Ῥ |
ῥ |
ῥ |
ῤ |
ῤ |
Named character reference | Ρ | ρ | ||||||||
DOS Greek | 144 | 90 | 168 | A8 | ||||||
DOS Greek-2 | 199 | C7 | 235 | EB | ||||||
Windows 1253 | 209 | D1 | 241 | F1 | ||||||
TeX | \rho |
Greek rho symbols
Preview | ϱ | ϼ | ᴩ | ᵨ | ☧ | |||||
---|---|---|---|---|---|---|---|---|---|---|
Unicode name | GREEK RHO SYMBOL | GREEK RHO WITH STROKE SYMBOL | GREEK LETTER SMALL CAPITAL RHO | GREEK SUBSCRIPT SMALL LETTER RHO | CHI RHO | |||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex | dec | hex |
Unicode | 1009 | U+03F1 | 1020 | U+03FC | 7465 | U+1D29 | 7528 | U+1D68 | 9767 | U+2627 |
UTF-8 | 207 177 | CF B1 | 207 188 | CF BC | 225 180 169 | E1 B4 A9 | 225 181 168 | E1 B5 A8 | 226 152 167 | E2 98 A7 |
Numeric character reference | ϱ |
ϱ |
ϼ |
ϼ |
ᴩ |
ᴩ |
ᵨ |
ᵨ |
☧ |
☧ |
Named character reference | ϱ, ϱ | |||||||||
TeX | \varrho |
Coptic ro
Preview | Ⲣ | ⲣ | ⳩ | |||
---|---|---|---|---|---|---|
Unicode name | COPTIC CAPITAL LETTER RO | COPTIC SMALL LETTER RO | COPTIC SYMBOL CHI RHO | |||
Encodings | decimal | hex | dec | hex | dec | hex |
Unicode | 11426 | U+2CA2 | 11427 | U+2CA3 | 11497 | U+2CE9 |
UTF-8 | 226 178 162 | E2 B2 A2 | 226 178 163 | E2 B2 A3 | 226 179 169 | E2 B3 A9 |
Numeric character reference | Ⲣ |
Ⲣ |
ⲣ |
ⲣ |
⳩ |
⳩ |
Functional symbol
Preview | ⍴ | |
---|---|---|
Unicode name | APL FUNCTIONAL SYMBOL RHO | |
Encodings | decimal | hex |
Unicode | 9076 | U+2374 |
UTF-8 | 226 141 180 | E2 8D B4 |
Numeric character reference | ⍴ |
⍴ |
Mathematical rho
Preview | 𝚸 | 𝛒 | 𝛠 | 𝛲 | 𝜌 | |||||
---|---|---|---|---|---|---|---|---|---|---|
Unicode name | MATHEMATICAL BOLD CAPITAL RHO |
MATHEMATICAL BOLD SMALL RHO |
MATHEMATICAL BOLD RHO SYMBOL |
MATHEMATICAL ITALIC CAPITAL RHO |
MATHEMATICAL ITALIC SMALL RHO | |||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex | dec | hex |
Unicode | 120504 | U+1D6B8 | 120530 | U+1D6D2 | 120544 | U+1D6E0 | 120562 | U+1D6F2 | 120588 | U+1D70C |
UTF-8 | 240 157 154 184 | F0 9D 9A B8 | 240 157 155 146 | F0 9D 9B 92 | 240 157 155 160 | F0 9D 9B A0 | 240 157 155 178 | F0 9D 9B B2 | 240 157 156 140 | F0 9D 9C 8C |
UTF-16 | 55349 57016 | D835 DEB8 | 55349 57042 | D835 DED2 | 55349 57056 | D835 DEE0 | 55349 57074 | D835 DEF2 | 55349 57100 | D835 DF0C |
Numeric character reference | 𝚸 |
𝚸 |
𝛒 |
𝛒 |
𝛠 |
𝛠 |
𝛲 |
𝛲 |
𝜌 |
𝜌 |
Preview | 𝜚 | 𝜬 | 𝝆 | 𝝔 | 𝝦 | |||||
---|---|---|---|---|---|---|---|---|---|---|
Unicode name | MATHEMATICAL ITALIC RHO SYMBOL |
MATHEMATICAL BOLD ITALIC CAPITAL RHO |
MATHEMATICAL BOLD ITALIC SMALL RHO |
MATHEMATICAL BOLD ITALIC RHO SYMBOL |
MATHEMATICAL SANS-SERIF BOLD CAPITAL RHO | |||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex | dec | hex |
Unicode | 120602 | U+1D71A | 120620 | U+1D72C | 120646 | U+1D746 | 120660 | U+1D754 | 120678 | U+1D766 |
UTF-8 | 240 157 156 154 | F0 9D 9C 9A | 240 157 156 172 | F0 9D 9C AC | 240 157 157 134 | F0 9D 9D 86 | 240 157 157 148 | F0 9D 9D 94 | 240 157 157 166 | F0 9D 9D A6 |
UTF-16 | 55349 57114 | D835 DF1A | 55349 57132 | D835 DF2C | 55349 57158 | D835 DF46 | 55349 57172 | D835 DF54 | 55349 57190 | D835 DF66 |
Numeric character reference | 𝜚 |
𝜚 |
𝜬 |
𝜬 |
𝝆 |
𝝆 |
𝝔 |
𝝔 |
𝝦 |
𝝦 |
Preview | 𝞀 | 𝞎 | 𝞠 | 𝞺 | 𝟈 | |||||
---|---|---|---|---|---|---|---|---|---|---|
Unicode name | MATHEMATICAL SANS-SERIF BOLD SMALL RHO |
MATHEMATICAL SANS-SERIF BOLD RHO SYMBOL |
MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL RHO |
MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL RHO |
MATHEMATICAL SANS-SERIF BOLD ITALIC RHO SYMBOL | |||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex | dec | hex |
Unicode | 120704 | U+1D780 | 120718 | U+1D78E | 120736 | U+1D7A0 | 120762 | U+1D7BA | 120776 | U+1D7C8 |
UTF-8 | 240 157 158 128 | F0 9D 9E 80 | 240 157 158 142 | F0 9D 9E 8E | 240 157 158 160 | F0 9D 9E A0 | 240 157 158 186 | F0 9D 9E BA | 240 157 159 136 | F0 9D 9F 88 |
UTF-16 | 55349 57216 | D835 DF80 | 55349 57230 | D835 DF8E | 55349 57248 | D835 DFA0 | 55349 57274 | D835 DFBA | 55349 57288 | D835 DFC8 |
Numeric character reference | 𝞀 |
𝞀 |
𝞎 |
𝞎 |
𝞠 |
𝞠 |
𝞺 |
𝞺 |
𝟈 |
𝟈 |
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
References
- ^ Paul of Aegina explains conventional usage in the last chapter of Book VII on weights and measures and uses it throughout his work.
- ^ Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)