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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ξ | xi

The Greek letter ξ (xi) was derived from the ancient Phoenician letter 𐤎 (sāmek), which, in its turn, could have evolved from the Egyptian hieroglyph 𓊽 (djed), representing the spinal column. Other theories say 𐤎 meant “fish” (actually showing a fish skeleton?) or “a tent peg”.

The lower-case ξ has a number of uses in maths and sciences, including

• in astronomy: the correlation function ξ(r)
• in natural product chemistry: to denote unknown configuration (which could be either α or β) at a chiral centre
• in mathematics: the remainder term of Taylor’s theorem
• in physical chemistry: the extent of reaction
• in physics: the spatial frequency (the reciprocal of the wavelength λ)

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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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〇 | líng

In Mandarin Chinese, 〇 (Pinyin: líng 🔊) is a word for number zero.

In AD 690, Wu Zetian (624—705), the only Empress Regnant in the history of China, adopted a number of new characters, one of which was 〇. Originally, it was meant to replace the unwieldy character 星 “star”. After the Empress’s death, the new characters fell into disuse. In 1247, Qin Jiushao (ca. 1202—1261) found a new job for 〇. It was introduced as the symbol for zero in his work 數書九章 (Shùshū Jiǔzhāng, “Mathematical Treatise in Nine Sections”). Another hanzi with the same meaning, 零, is mainly used for financial purposes.

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0 | zero

Probably the first documented use of a number zero in the Old World was by Claudius Ptolemy in the Almagest (ca. 130 AD), although in the Americas the concept and symbol for zero existed much earlier.

Ptolemy employed the symbol ο̄ (“Hellenistic zero”) within a Babylonian sexagesimal numeral system. The oldest known mention of zero and the decimal positional system are found in the Jainist cosmological text Lokavibhāga (AD 458). By the 11^th century, the Hindu–Arabic numeral system, complete with zero, reached Europe.

In my handwriting, I almost always write this digit as a slashed zero, 0.

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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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η | eta

The Greek letter η (eta) was derived from the ancient Phoenician letter 𐤇 (ḥēt) which, in turn, was derived from an Egyptian hieroglyph of courtyard, 𓉗.

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

• in coordination chemistry: a symbol for hapticity
• in cosmology: the baryon–photon ratio
• in mathematics: the Dedekind eta function η(τ), the Dirichlet eta function η(s), and the Weierstrass eta function η(w; Λ)
• in particle physics: symbols for eta meson (η), eta prime meson (η′), charmed eta meson (η_c) and bottom eta meson (η_b)
• in rheology: a symbol for viscosity

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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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