ψ | psi

The letter ψ (psi) was yet another Greek addition to the alphabet, placed after the letters of Phoenician origin, along with φ, χ and ω. According to Wikipedia,

The letter’s origin is uncertain. It may or may not derive from the Phoenician alphabet. It appears in the 7^th century BC, expressing /ps/ in the Eastern alphabets, but /kʰ/ in the Western alphabets (the sound expressed by Χ in the Eastern alphabets).

The letter ψ has a number of uses in maths and sciences, including

• in biochemistry: pseudouridine
• in carotenoid nomenclature: acyclic end group. For example, lycopene is ψ,ψ-carotene.
• in hydrostatics and biology: water potential
• in fluid mechanics: stream function
• in mathematics: the division polynomials ψ_n
• in mathematics: the polygamma function
• in mathematics: the reciprocal Fibonacci constant with approximate value of 3.35989
• in molecular biology: the ψ packaging element
• in particle physics: the J/ψ meson (psion)
• in protein chemistry: one of three dihedral angles (φ, ψ and ω) in a protein chain
• in quantum mechanics: wave function

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χ | chi

The letter χ (chi) was a Greek addition to the alphabet, placed after the letters of Phoenician origin, along with φ, ψ and ω. According to Wikipedia,

In Ancient Greek, ‘Χ’ and ‘Ψ’ were among several variants of the same letter, used originally for /kʰ/ and later, in western areas such as Arcadia, as a simplification of the digraph ‘ΧΣ’ for /ks/. In the end, more conservative eastern forms became the standard of Classical Greek, and thus ‘Χ’ (Chi) stands for /kʰ/ (later /x/). However, the Etruscans had taken over ‘Χ’ from western Greek, and it therefore stands for /ks/ in Etruscan and Latin.

The Greek χ gave rise to the Latin X, Gothic enguz 𐍇 and Cyrillic Х.

The lower-case χ has a number of uses in maths and sciences:

• in biology: Chi site or χ site, a DNA sequence that serves as a recombination hot spot (“Chi” is an abbreviation of “crossover hotspot instigator”)
• in chemistry: electronegativity
• in graph theory: chromatic number χ(G) for a graph G
• in mathematics: the Euler–Poincaré characteristic of a surface
• in statistics: χ² or chi-square
• in thermodynamics: a free energy parameter known as the χ-parameter, employed in the Flory–Huggins solution theory

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μ | mu

The Greek letter μ (mu) arose from the ancient Phoenician letter 𐤌 (mēm) which, in turn, was derived from the Egyptian hieroglyph for water, 𓈖.

The lower-case μ has many uses in maths, engineering and sciences, for example:

• in coordination chemistry: μ-, a prefix for a bridging ligand
• in electromagnetism:
  • the magnetic moment and the units to express it, such as the Bohr magneton μ_B and the nuclear magneton μ_N
  • the permeability µ, measured in henries per meter (H·m⁻¹);
  • the vacuum permeability or magnetic constant µ₀, which has the exact value of 4π×10⁻⁷ H·m⁻¹
• in fluid mechanics: dynamic viscosity
• in mathematics: the Möbius function μ(n)
• in maths and physics: µ (micro-), a unit prefix in the metric system for 10⁻⁶ (one millionth)
• in particle physics: muon μ⁻ and antimuuon μ⁺ (formerly called μ-mesons)
• in pharmacology: μ-opioid receptor (MOR)
• in physics: the coefficient of friction
• in physics: the electrical_mobility of a charged particle
• in thermodynamics: chemical potential aka partial molar free energy μ_i

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τ | tau

The Greek letter τ (tau) was derived from the ancient Phoenician letter 𐤕 (tāw) which, in turn, was derived from an Egyptian hieroglyph ✕ meaning “mark”.

The lower-case τ has many uses in maths, engineering and sciences, such as

• in biochemistry: the τ protein, a protein that stabilise microtubules
• in continuum mechanics: shear stress
• in differential geometry: torsion of a curve
• in engineering and physics: the time constant of a system
• in geometry: the tortuosity
• in mathematics: the Ramanujan tau function, an irrational number with approximate value of 0.41468
• in mechanics: the torque, aka moment of force
• in optics: optical depth of a material, defined as τ = −ln T, where T is the transmittance of that material
• in particle physics: tauon τ⁻ and antitauon τ⁺
• in physical sciences: relaxation time
• in physics: the lifetime of a spontaneous emission process
• in relativity: proper time
• in spectroscopy: rotational correlation time
• in statistics: the Kendall rank correlation coefficient

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ω | omega

The letter ω (omega) is the 24^th and last letter of the Greek alphabet. It was first introduced in the 7^th century BC as a broken-up at the side variant of omicron. This letter was adopted into the early Cyrillic alphabet as Cyrillic omega (Ѡ, ѡ), with both upper- and lower-case letters similar to the Greek lower-case ω.

The lower-case ω has quite a few uses in maths, engineering and sciences, for example

• in astronomy: the argument of periapsis of an orbit
• in biochemistry: to denote the carbon atom furthest from the carboxyl group of a fatty acid. “ω−i fatty acid” is an unsaturated fatty acid with a double bond (C=C) at the i^th carbon atom from the end, as in ω−3 fatty acids, ω−7 fatty acids, etc.
• in electrical circuits: natural frequency ω₀
• in molecular biology: the smallest subunit of RNA polymerase
• in number theory: ω(n), the number of distinct prime factors of n
• in particle physics: omega meson
• in physics: angular frequency and angular velocity
• in protein chemistry: one of three dihedral angles (φ, ψ and ω) in a protein chain. ω is usually restricted to be 180° (trans) or 0° (cis).

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ρ | rho

The Greek letter ρ (rho) was derived from the ancient Phoenician letter 𐤓 (rēš), which is thought to have come from a pictogram of a head. As a numeral, ρ has a value of 100. Incidentally, this is our 100^th post.

The lower-case ρ (or its variant ϱ) has many uses in maths and sciences, such as:

• in electrical engineering and physics: resistivity (the reciprocal of conductivity σ)
• in electromagnetism: the volume charge density, ρ_q
• in molecular biology: the ρ factor, a protein involved in the termination of transcription
• in mathematics: the Dickman–de Bruijn function ρ(u)
• in mathematics: the plastic number, a constant with approximate value of 1.32472, the unique real solution of the cubic equation x³ = x + 1
• in mathematics: the prime constant, an irrational number with approximate value of 0.41468
• in mathematics: ρ(A), the spectral radius of a matrix A
• in organic chemistry: ρ-value (the reaction constant) of the Hammett equation
• in particle physics: rho mesons ρ⁺, ρ⁰ and ρ⁻
• in physics: mass density and air density
• in spectroscopy: rotational relaxation time
• in statistics: the Pearson correlation coefficient

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σ | sigma

The Greek letter σ (sigma) was derived from the ancient Phoenician letter 𐤔 (šīn) which meant “tooth”.

ς is the lower-case letter sigma (σίγμα τελικό) when used as the final letter in a word.

The lower-case σ has been widely adopted in maths and sciences, for instance:

• in chemistry: the σ bonds
• in continuum mechanics: the Cauchy stress tensor σ
• in biochemistry: σ factor of RNA polymerase
• in mathematics: σ(z; Λ), the Weierstrass sigma function
• in organic chemistry: σ-value (the substituent constant) of the Hammett equation
• in particle physics: cross section
• in pharmacology: the σ–receptors
• in physics: the surface charge density, σ_q
• in physics: a symbol for conductivity (the reciprocal of resistivity ρ)
• in statistics: the standard deviation
• in thermodynamics: the Stefan–Boltzmann constant

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λ | lambda

The Greek letter λ (lambda) was derived from the ancient Phoenician letter 𐤋 (lāmed) which meant “goad” (a cattle prod).

The lower-case letter λ has many uses in maths, engineering and sciences, including:

• in biology: coliphage λ
• in engineering, mathematics and physics: the wavelength
• in mathematical logic: λ-calculus
• in organic chemistry: λ-convention for non-standard valence states
• in immunology: a type of the immunoglobulin light chain
• in linear algebra: an eigenvalue
• in nuclear physics: the exponential decay constant
• in physics: the linear charge density, λ_q

λ is also one of the international symbols for LGBT rights.

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κ | kappa

The Greek letter κ (kappa) was derived from the ancient Phoenician letter 𐤊 (kāp) which meant “palm” (of a hand).

The lower-case κ is pretty much just a smaller version of the upper-case Κ and is virtually indistinguishable from the upper-case Roman K as well as the Cyrillic К/к. I prefer using the cursive ϰ.

The lower-case κ and/or cursive ϰ have quite a few uses in maths, engineering and sciences, for instance:

• in coordination chemistry: a symbol for denticity
• in geometry: kappa curve, or Gutschoven’s curve, a two-dimensional curve resembling the letter ϰ
• in electrical engineering: conductivity (the reciprocal of resistivity ρ)
• in fluid dynamics: the von Kármán constant
• in immunology: a type of the immunoglobulin light chain
• in mathematics and physics: the curvature
• in pharmacology: κ-opioid receptor (KOR)
• in statistics: Cohen’s kappa coefficient

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ι | iota

The Greek letter ι (iota) was derived from the ancient Phoenician letter 𐤉 (yōd) which meant “arm”. The archaic Cyrillic iota ꙇ looks exactly the same.

The lower-case ι looks too similar to the Latin letters i and l to be widely used as a symbol on its own. Still, it has been adopted in maths and sciences, for instance:

• in biochemistry: ι-toxin, a pore forming toxin from Clostridium perfringens
• in mathematical logic: a definite description operator
• in natural product chemistry: ι-carrageenan, a polysaccharide extracted from red algae that gels in the presence of calcium ions

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θ | theta

The Greek letter θ (theta) was derived from the ancient Phoenician letter 𐤈 (ṭēt) which meant “wheel”. The Cyrillic letter Ѳ (fita), derived from θ, was a part of the Russian alphabet until 1918. Gogol wrote in a footnote to Dead Souls:

«Ѳетюкъ — слово обидное для мужчины, происходитъ отъ Ѳ, буквы, почитаемой нѣкоторыми неприличною буквою.»

(“Thetuk” is an offensive word to a man, it comes from Ѳ, a letter thought by some indecent.)

Speaking of decency: according to Real Academia Española, this letter should be called zeta, perhaps to avoid using the word teta, while the letter ζ is supposed to be called dseta.

The lower-case letter θ has quite a few uses in maths and sciences, for instance:

• in astronomy, geography, mathematics and physics: one of the coordinates in spherical coordinate system (r, θ, φ)
• in neurophysiology: θ-waves, a type of brain waves detected by electroencephalography
• in linguistics: θ-role
• in mathematics: a number of different fuctions called theta functions
• in particle physics: symbol for theta meson
• in phonetics: voiceless dental fricative, as in theta /ˈθiːtə/ or /ˈθeɪtə/
• in thermodynamics: a symbol for potential temperature

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ζ | zeta

The Greek letter ζ (zeta) was derived from the ancient Phoenician letter 𐤆 (zayin) which meant “sword” or some other weapon.

In the system of Greek numerals, the letters α to ε have the respective values 1 through 5. Bizarrely, ζ has the value of 7. This may account for the fact that chemists don’t like using Greek letters beyond ε when numbering the atoms in the chain. Still, the lower-case letter ζ has some uses in maths and sciences, for example:

• in colloidal chemistry: ε_i, ζ-potential, the electrokinetic potential of colloidal dispersions
• in mathematics: ζ(s), the Euler–Riemann zeta function
• in mathematics: ζ(z; Λ), the Weierstrass zeta function
• in pharmacology: ζ-opioid receptor, aka opioid growth factor receptor

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ε | epsilon

The Greek letter ε (epsilon) was derived from the ancient Phoenician letter 𐤄 (hē) which meant “window”. In its turn, ε gave rise to the Latin e and a number of other letters.

The lower-case letter ε has a number of uses in maths and sciences:

• in analytical chemistry: ε_i, molar attenuation coefficient, also known as the molar extinction coefficient and molar absorptivity
• in astronomy: the fifth brightest star in a constellation. For instance, Alnilam is designated as ε Orionis.
• in calculus: (ε, δ)-definition of limit
• in medicine: ε-wave, a feature of electrocardiograms of many arrhythmogenic right ventricular dysplasia (ARVC) patients
• in organic chemistry: ε, the fifth atom in a chain when counting from a functional group. The names such as ε-aminocaproic acid make use of this nomenclature.
• in phonetics: Latin epsilon, ɛ, representing the open-mid front unrounded vowel, as in epsilon /ɛpˈsaɪ.lən/ or /ˈɛp.sɪˌlɒn/
• in physics: ε₀, vacuum permittivity constant

α through ɛ appears to be the extent to which most people know the letter sequence of the Greek alphabet.

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δ | delta

The Greek letter δ (delta) was derived from the ancient Phoenician letter 𐤃 (dālet) which, in turn, was derived from 𓉿, an Egyptian hieroglyph depicting a door.

The lower-case letter δ has many uses in maths and sciences, such as:

• in astronomy: the fourth brightest star in a constellation. For instance, Mintaka is designated as δ Orionis.
• in chemistry: δ bond, a type of covalent chemical bond formed by overlapping lobes of d orbitals
• in chemistry: a symbol for partial charge, δ− or δ+
• in earth sciences: to express stable isotope ratios, for example δ²H, δ¹³C, δ¹⁸O
• in mathematics: δ, the first Feigenbaum constant (approximately 4.669201)
• in maths and science: Dirac δ function
• in neurophysiology: δ-waves, a type of brain waves detected by electroencephalography
• in pharmacology: a type of opioid receptor
• in thermodynamics: inexact differential. For example, the first law of thermodynamics is expressed as

  dU = δQ – δW

  where U is internal energy, Q is heat and W is work.

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γ | gamma

The Greek letter γ (gamma) was derived from the ancient Phoenician letter 𐤂 (gīml). One theory says that it represented a throwing stick, another links it to (an image of) a camel.

The lower-case letter γ has a number of uses in maths and sciences, for example:

• in astronomy: the third brightest star in a constellation. For instance, Bellatrix is designated as γ Orionis.
• in inorganic chemistry: a symbol for certain allotropes, for example γ-iron (austenite) or γ-sulfur
• in mathematics: the Euler—Mascheroni constant, a mathematical constant with approximate value of 0.57721
• in organic chemistry: γ-carbon, the third carbon atom in a chain when counting from a functional group. The names such as γ-aminobutyric acid (GABA) make use of this nomenclature.
• in neurophysiology: γ-waves, a type of brain waves detected by electroencephalography
• in phonetics: voiced velar fricative (IPA symbol ɣ)
• in physics: γ is the symbol for a photon, probably derived from γ-rays or γ-radiation, a kind of electromagnetic radiation arising from the radioactive decay (γ-decay)
• in special relativity: Lorentz factor

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β | beta

The Greek letter β (beta) was derived from the ancient Phoenician letter 𐤁 (bet). The word alphabet originates from the Greek ἀλφάβητος (alphabētos), from ἄλφα (“alpha”) + βῆτα (“beta”).

The lower-case letter β has found many uses in maths and sciences:

• in astronomy: the second brightest star in a constellation. For instance, Rigel is designated as β Orionis
• in biochemistry: β-sheet, a type of protein secondary structure
• in biology: β cell, a type of cell found in the pancreatic islets of the pancreas. The primary function of a β cell is to produce insulin.
• in inorganic chemistry: a symbol for certain allotropes, for example β-tetragonal boron, β-germanium, and β-tin
• in mathematics: β(s), the Dirichlet beta function
• in natural product chemistry: a stereodescriptor used in a number of different ways
• in nuclear physics: beta particle, a high-energy electron (β⁻) or positron (β⁺) emitted in the radioactive decay; β-decay is a radioactive process in which an atomic nucleus emits an β-particle
• in organic chemistry: β-carbon, the second carbon atom in a chain when counting from a functional group
• in pharmacology: β₁, β₂ and β₃, subtypes of adrenergic receptors
• in phonetics: voiced bilabial fricative (IPA symbol β)
• in special relativity: a symbol for the speed of an object relative to the speed of light: β = v/c
• in thermodynamics and fluid mechanics: a symbol for compressibility
• in zoology: β animals, which often act as second-in-command to the reigning α-males and/or α-females

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α | alpha

The Greek letter α (alpha) was derived from the ancient Phoenician letter 𐤀 (ʾālep) which, in turn, was derived from 𓃾, the Egyptian hieroglyph of an ox’s head.

The lower-case letter α has found many uses in maths and sciences:

• in astronomy: the brightest star in a constellation. For instance, Betelgeuse is designated as α Orionis
• in biochemistry: α-helix, a type of protein secondary structure
• in inorganic chemistry: a symbol for certain (usually the most common) allotropes, for example α-iron, α-phosphorus, and α-sulphur
• in natural product chemistry: a stereodescriptor used in a number of different ways
• in navigation: a symbol for azimuth
• in neurophysiology: α-waves, a type of brain waves detected by electroencephalography
• in nuclear physics: alpha particle, α or α²⁺, a historical name of doubly ionised helium nuclei (He²⁺) ; α-decay is a radioactive process in which an atomic nucleus emits an α-particle
• in organic chemistry: the α-carbon is the first carbon atom attached to a functional group; α-amino acids are amino acids with an amino group bound directly to the α-carbon
• in pharmacology: α₁ and α₂, subtypes of adrenergic receptors
• in physics: a symbol for angular acceleration
• in physics: the fine-structure constant
• in zoology: α-males and α-females, the highest ranking individuals in a community of social animals

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