Greek letters used in mathematics, science, and engineering (original) (raw)

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Symbols for constants, special functions

Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities. Those Greek letters which have the same form as Latin letters are rarely used: capital Α, Β, Ε, Ζ, Η, Ι, Κ, Μ, Ν, Ο, Ρ, Τ, Υ, and Χ. Small ι, ο and υ are also rarely used, since they closely resemble the Latin letters i, o and u. Sometimes, font variants of Greek letters are used as distinct symbols in mathematics, in particular for ε/ϵ and π/ϖ. The archaic letter digamma (Ϝ/ϝ/ϛ) is sometimes used.

The Bayer designation naming scheme for stars typically uses the first Greek letter, α, for the brightest star in each constellation, and runs through the alphabet before switching to Latin letters.

In mathematical finance, the Greeks are the variables denoted by Greek letters used to describe the risk of certain investments.

Some common conventions:

• Intensive quantities in physics are usually denoted with minuscules
  while extensive are denoted with capital letters.
• Most symbols are written in italics.
• Vectors can be denoted in boldface.
• Sets of numbers are typically bold or blackboard bold.

The Greek letter forms used in mathematics are often different from those used in Greek-language text: they are designed to be used in isolation, not connected to other letters, and some use variant forms which are not normally used in current Greek typography.

The OpenType font format has the feature tag "mgrk" ("Mathematical Greek") to identify a glyph as representing a Greek letter to be used in mathematical (as opposed to Greek language) contexts.

The table below shows a comparison of Greek letters rendered in TeX and HTML. The font used in the TeX rendering is an italic style. This is in line with the convention that variables should be italicized. As Greek letters are more often than not used as variables in mathematical formulas, a Greek letter appearing similar to the TeX rendering is more likely to be encountered in works involving mathematics.

Concepts represented by a Greek letter

[edit]

• α {\displaystyle \alpha } represents:
  • the first angle in a triangle, opposite the side a
  • the statistical significance of a result
  • the false positive rate in statistics ("Type I" error)[1]
  • the fine-structure constant in physics[2][3]
  • the angle of attack of an aircraft
  • an alpha particle (He2+)
  • angular acceleration in physics[4]
  • the linear thermal expansion coefficient
  • the thermal diffusivity[5]
  • In organic chemistry the α-carbon is the backbone carbon next to the carbonyl carbon, most often for amino acids
  • right ascension in astronomy[6]
  • the brightest star in a constellation[7]
  • Iron ferrite and numerous phases within materials science
  • the return in excess of the compensation for the risk borne in investment
  • the α-conversion in lambda calculus
  • the independence number of a graph
  • a placeholder for ordinal numbers in mathematical logic
  • a type of receptor for the neurotransmitter noradrenaline in neuroscience
• ϵ {\displaystyle \epsilon } represents:
  • a small positive quantity; see limit
  • a random error in regression analysis
  • the absolute value of an error[26]
  • in set theory, the limit ordinal of the sequence ω , ω ω , ω ω ω , … {\displaystyle \omega ,\omega ^{\omega },\omega ^{\omega ^{\omega }},\dots }
  • in computer science, the empty string
  • the Levi-Civita symbol
  • in electromagnetics, dielectric permittivity[27]
  • emissivity
  • strain in continuum mechanics
  • permittivity[28]
  • the Earth's axial tilt in astronomy[29]
  • elasticity in economics[30]
  • electromotive force
  • in chemistry, the molar extinction coefficient of a chromophore
  • in mathematics, a surreal number that is bigger than zero, but smaller than all positive real numbers.
• set membership symbol ∈ is based on ε
• Ϝ is sometimes used to represent the digamma function, though the Latin letter F (which is nearly identical) is usually substituted.
• A hypothetical particle Ϝ speculated to be implicated in the 750 GeV diphoton excess, now known to be simply a statistical anomaly
• ζ {\displaystyle \zeta } represents:
  • the Riemann zeta function and other zeta functions in mathematics
  • the damping ratio[31]
  • the value for the Zeta potential, i.e., the electrical potential at the slipping plane, used often in colloidal chemistry[32]
• ι {\displaystyle \iota } represents:
  • an inclusion map in set theory
  • the index generator function in APL (in the form ⍳)
  • the interior product
  • an imaginary number
• μ {\displaystyle \mu } represents:
  • the Möbius function in number theory
  • the population mean or expected value in probability and statistics
  • a measure in measure theory
  • micro-, an SI prefix denoting 10−6 (one millionth)
  • Micrometre or micron (retired in 1967 as a standalone symbol, replaced by "μm" using the standard SI meaning)
  • the coefficient of friction in physics
  • the service rate in queueing theory
  • the dynamic viscosity in physics
  • magnetic permeability in electromagnetics[48]
  • a muon[49]
  • reduced mass[50]
  • the ion mobility in plasma physics
  • the Standard gravitational parameter in celestial mechanics
  • population mean in statistics
  • chemical potential in thermodynamics
  • Absorption coefficient
  • Amplification factor
  • Magnetic moment of a dipole[51]
• ν {\displaystyle \nu } represents:
  • frequency in physics in hertz (Hz)
  • Poisson's ratio in materials science
  • a neutrino[52]
  • kinematic viscosity of liquids[53]
  • stoichiometric coefficient in chemistry
  • true anomaly in celestial mechanics[54]
  • degrees of freedom in statistics
  • the matching number of a graph
  • the p-adic valuation of a number
• Π {\displaystyle \Pi } represents:
  • the product operator in mathematics
  • a plane
  • the unary projection operation in relational algebra
  • the Pi function, i.e. the Gamma function when offset to coincide with the factorial
  • the complete elliptic integral of the third kind
  • the fundamental groupoid
  • osmotic pressure
• π {\displaystyle \pi } represents:
  • Archimedes' constant (more commonly just called Pi), the ratio of a circle's circumference to its diameter
  • the prime-counting function
  • the state distribution of a Markov chain
  • in reinforcement learning, a policy function defining how a software agent behaves for each possible state of its environment
  • a type of covalent bond in chemistry (pi bond)
  • a pion (pi meson) in particle physics
  • in statistics, the population proportion
  • nucleotide diversity in molecular genetics
  • in electronics, a special type of small-signal model is referred to as a hybrid-pi model
  • in discrete mathematics, a permutation
  • Projection
• ϖ (a graphic variant, see pomega) represents:
  • angular frequency of a wave, in fluid dynamics (angular frequency is usually represented by ω {\displaystyle \omega } but this may be confused with vorticity in a fluid dynamics context)
  • longitude of pericenter, in astronomy[55]
  • comoving distance, in cosmology[56]
• τ {\displaystyle \tau } represents:
  • torque, the net rotational force in mechanics
  • the elementary tau lepton in particle physics
  • a mean lifetime, of an exponential decay or spontaneous emission process
  • the time constant of any device, such as an RC circuit
  • proper time in relativity
  • one turn: the constant ratio of a circle's circumference to its radius, with value 2 π {\displaystyle 2\pi } (6.283...).[62]
  • Kendall tau rank correlation coefficient, a measure of rank correlation in statistics
  • Ramanujan's tau function in number theory
  • shear stress in continuum mechanics[63]
  • a type variable in type theories, such as the simply typed lambda calculus
  • path tortuosity in reservoir engineering
  • in topology, a given topology
  • the tau in biochemistry, a protein associated to microtubules
  • the number of divisors of highly composite numbers (sequence A000005 in the OEIS)
  • precision ( τ 2 {\displaystyle \tau ^{2}} ), the reciprocal of variance, in statistics
• Υ {\displaystyle \Upsilon } (U+03D2) represents:
  • the upsilon meson
• Φ {\displaystyle \Phi } represents:

Note: The empty set symbol ∅ looks similar, but is unrelated to the Greek letter.

• Blackboard bold letters used in mathematics
• English pronunciation of Greek letters
• Latin letters used in mathematics, science, and engineering
• List of letters used in mathematics, science, and engineering
• Glossary of mathematical symbols
• Mathematical Alphanumeric Symbols (a Unicode block)
• Mathematical notation
• Greek alphabet

1. ^ Lindenmayer, David. (2005). Practical conservation biology. Burgman, Mark A. Collingwood, Vic.: CSIRO Pub. p. 404. ISBN 0-643-09310-9. OCLC 65216357. These parameters are related by the expression:… where E is effect size, n is sample size, α is the type I error rate and σ is the standard deviation of the variability of the data
2. ^ "fine-structure constant". physics.nist.gov. Retrieved 2025-02-10.
3. ^ Rabinowitz, Harold; Vogel, Suzanne (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam Burlington, MA: Elsevier/Academic Press. p. 348. ISBN 978-0-12-373980-3.
4. ^ Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 793. ISBN 978-0-12-373980-3. OCLC 156811865.
5. ^ Lamond, Joseph F.; Pielert, J. H., eds. (2006). Significance of tests and properties of concrete and concrete-making materials. STP (Rev. ed.). Philadelphia, PA: ASTM. p. 229. ISBN 978-0-8031-3367-9. OCLC 69865403. Thermal diffusivity is defined numerically as thermal conductivity divided by the product of specific heat and density, or α= k/ (CxP)
6. ^ Burns, M. Shane (2022). A practical guide to observational astronomy (First ed.). Boca Raton: CRC Press. p. 5. ISBN 978-0-367-76863-8. The two angles that specify the location of a point on the celestial sphere are called the right ascension α and the declination δ
7. ^ Rabinowitz, Harold; Vogel, Suzanne (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam Burlington, MA: Elsevier/Academic Press. p. 363. ISBN 978-0-12-373980-3. The primary designation system for bright stars, called Bayer designations… The Greek letters are assigned in order (α,β, γ,δ etc.) according to brightness.
8. ^ Bhandari, Pritha (2021-01-18). "Type I & Type II Errors | Differences, Examples, Visualizations". Scribbr. Retrieved 2025-01-22. The probability of making a Type I error is the significance level, or alpha (α), while the probability of making a Type II error is beta (β).
9. ^ Languis, M. L.; Buffer, James J.; Martin, Daniel; Naour, Paul J. (2011). Cognitive Science (RLE Edu E): Contributions to Educational Practice. Routledge Library Editions: Education. Hoboken: Taylor and Francis. p. 183. ISBN 978-0-415-68351-7. Vieth (1982) established that cognition could be quantified by summing the value of alpha plus beta brain waves.
10. ^ Bowen, Alan C.; Rochberg, Francesca, eds. (2020). Hellenistic astronomy: the science in its contexts. Brill's companions in classical studies. Leiden ; Boston: Brill. pp. 16–17. ISBN 978-90-04-24336-1. Celestial longitude (λ) is measured eastward from the vernal equinox along the zodiacal circle, and celestial latitude (β) is the angular distance of the arc dropped perpendicularly from the body to the zodiacal circle.
11. ^ Freidberg, Jeffrey P. (2014). Ideal MHD (1st ed.). West Nyack: Cambridge University Press. p. 68. ISBN 978-1-107-00625-6. The quantity β is a global plasma parameter whose value is critical for a fusion reactor... Qualitatively, β measures the ratio plasma pressure to magnetic pressure:
12. ^ Volchenkov, Dimitri (2022). Mathematical Methods in Modern Complexity Science. Nonlinear Systems and Complexity Series. José António Tenreiro Machado. Cham: Springer International Publishing AG. p. 36. ISBN 978-3-030-79411-8. We defined β as the ratio v/c, where v the is the modulus of the vector velocity v.
13. ^ Zhang, Keqian; Li, Dejie, eds. (2008). Electromagnetic Theory for Microwaves and Optoelectronics. SpringerLink Bücher (2nd ed.). Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg. p. 82. ISBN 978-3-540-74295-1. The reflection coefficient Γis real when medium 1 and medium 2 are both lossless media,…
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15. ^ Hogg, Robert V.; Klugman, Stuart A. (2009). Loss Distributions. Wiley Series in Probability and Statistics. Hoboken: John Wiley & Sons, Inc. p. 225. ISBN 978-0-471-87929-9.
16. ^ Baumann, Gerd (2005). Mathematica for theoretical physics (2nd ed.). New York: Springer. p. 731. ISBN 978-0-387-01674-0.
17. ^ Kahle, Reinhard; Rathjen, Michael (2020). The legacy of Kurt Schütte. Cham: Springer. p. 41. ISBN 978-3-030-49423-0. The Veblen approach was quite sufficient even for the ordinal, now known as the Feferman–Schütte ordinal, Γ0 for predictive analysis
18. ^ "DLMF: §5.2 Definitions ‣ Properties ‣ Chapter 5 Gamma Function". dlmf.nist.gov. Retrieved 2025-01-31.
19. ^ Fayngold, Moses (2008). Special relativity and how it works. Physics textbook. Weinheim: Wiley-VCH. p. 32. ISBN 978-3-527-40607-4. Because we will come across this coefficient quite often, we will give it a special name, the Lorentz factor, and stick to our symbol γ(V),...
20. ^ Weisstein, Eric W. "Kronecker Delta". mathworld.wolfram.com. Retrieved 2025-01-23.
21. ^ Weisstein, Eric W. "Feigenbaum Constant". mathworld.wolfram.com. Retrieved 2025-01-23.
22. ^ Weisstein, Eric W. "Delta Function". mathworld.wolfram.com. Retrieved 2025-01-23.
23. ^ a b Katzung & Trevor's Pharmacology Examination & Board Review (9th Edition.). Anthony J. Trevor, Bertram G. Katzung, Susan B. Masters ISBN 978-0-07-170155-6. B. Opioid Peptides + 268 pp.
24. ^ Burns, M. Shane (2022). A practical guide to observational astronomy (First ed.). Boca Raton: CRC Press. p. 5. ISBN 978-0-367-76863-8. The two angles that specify the location of a point on the celestial sphere are called the right ascension α and the declination δ
25. ^ Kutner, Michael H.; Nachtsheim, Christopher J.; Neter, John; Li, William (2005). Applied Linear Statistical Models (5th ed.). New York: McGraw-Hill. pp. xxviii, 1396. ISBN 0-07-310874-X.
26. ^ Golub, Gene; Charles F. Van Loan (1996). Matrix Computations – Third Edition. Baltimore: The Johns Hopkins University Press. p. 53. ISBN 0-8018-5413-X.
27. ^ Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 346. ISBN 978-0-12-373980-3. OCLC 156811865.
28. ^ "Vacuum electric permittivity". physics.nist.gov. Retrieved 2025-02-10.
29. ^ Montenari, Michael, ed. (2018). Cyclostratigraphy and astrochronology. Stratigraphy and Timescales (1st ed.). London San Diego, Calif. Cambridge, Mass. Oxford: Academic Press, an imprint of Elsevier. p. 84. ISBN 978-0-12-815098-6. The Earth's orbital obliquity or axial tilt (ε) is the angle between the Earth's equatorial plane and its orbital plane,
30. ^ Free, Rhona C. (2010). 21st century economics: a reference handbook. Thousand Oaks (Calif.): Sage. pp. 93–94. ISBN 978-1-4129-6142-4.
31. ^ Wilkie, Jacqueline; Johnson, Michael; Katebi, Reza (2002). Control engineering: an introductory course. Basingstoke: Palgrave. p. 179. ISBN 978-0-333-77129-7. We shall refer to ζ as the damping ratio throughout this text.
32. ^ Hunter, Robert J. (1988). Zeta potential in colloid science: principles and applications (New paperback ed.). London San Diego: Academic Press. p. 6. ISBN 978-0-12-361961-7. It is also possible to correlate the ζ-potential with the sedimentation behaviour of colloidal systems and with the flotation behaviour of mineral ores.
33. ^ Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 346. ISBN 978-0-12-373980-3. OCLC 156811865.
34. ^ Harada, Kōichirō (2010). "Moonshine" of finite groups. EMS series of lectures in mathematics. Zürich: European Mathematical Society. p. 17. ISBN 978-3-03719-090-6.
35. ^ Struchtrup, Henning (2024). Thermodynamics and energy conversion (Second ed.). Cham: Springer. pp. 164–165. ISBN 978-3-031-60555-0.
36. ^ Rybicki, George B.; Lightman, Alan P. (1979). Radiative processes in astrophysics. A Wiley-Interscience publication. New York: Wiley. p. 123. ISBN 978-0-471-04815-2.
37. ^ Weisstein, Eric W. "Lambda Calculus". mathworld.wolfram.com. Retrieved 2025-01-22.
38. ^ Kubat, Miroslav (2021). An introduction to machine learning (Third ed.). Cham, Switzerland: Springer Nature. p. 129. ISBN 978-3-030-81934-7. When describing backpropagation of error, we assumed a constant learning rate, η .
39. ^ Weisstein, Eric W. "Kappa Curve". mathworld.wolfram.com. Retrieved 2025-02-06.
40. ^ Weisstein, Eric W. "Vertex Connectivity". mathworld.wolfram.com. Retrieved 2025-02-06.
41. ^ Weisstein, Eric W. "Curvature". mathworld.wolfram.com. Retrieved 2025-02-06.
42. ^ "Thermal Conductivity - Definition and Detailed Explanation". BYJUS. Retrieved 2025-02-06. It is generally denoted by the symbol 'k' but can also be denoted by 'λ' and 'κ'.
43. ^ Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 347. ISBN 978-0-12-373980-3. OCLC 156811865.
44. ^ "Einstein gravitational constant". Illuminating Science. Retrieved 2025-02-06.
45. ^ Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 347. ISBN 978-0-12-373980-3. OCLC 156811865.
46. ^ Bowen, Alan C.; Rochberg, Francesca, eds. (2020). Hellenistic astronomy: the science in its contexts. Brill's companions in classical studies. Leiden ; Boston: Brill. pp. 16–17. ISBN 978-90-04-24336-1. Celestial longitude (λ) is measured eastward from the vernal equinox along the zodiacal circle, and celestial latitude (β) is the angular distance of the arc dropped perpendicularly from the body to the zodiacal circle.
47. ^ "IR-6.2.1 Mononuclear parent hydrides with standard and non-standard bonding numbers". Nomenclature of Inorganic Chemistry (PDF). IUPAC Recommendations. IUPAC. 2005. pp. 84–86.
48. ^ "Vacuum magnetic permeability". physics.nist.gov. Retrieved 2025-02-10.
49. ^ Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 333. ISBN 978-0-12-373980-3. OCLC 156811865.
50. ^ Rabinowitz, Harold; Vogel, Suzanne (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam Burlington, MA: Elsevier/Academic Press. p. 346. ISBN 978-0-12-373980-3.
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54. ^ Grossman, Nathaniel (1996). The Sheer Joy of Celestial Mechanics. Boston, MA: Birkhäuser Boston. p. 75. ISBN 978-0-8176-3832-0. Introduce variables ζ and η related to the true anomaly f and the eccentric anomaly E by…
55. ^ Weisstein, Eric W. "Pomega -- from Eric Weisstein's World of Physics". scienceworld.wolfram.com. Retrieved 2022-09-06.
56. ^ Outline for Weeks 14&15, Astronomy 225 Spring 2008 Archived 2010-06-15 at the Wayback Machine
57. ^ Lebl, Jiří (May 16, 2022). Basic Analysis I, Introduction to Real Analysis. Vol. 1. p. 98. ISBN 978-1718862401.
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59. ^ "CODATA Value: Stefan-Boltzmann constant". physics.nist.gov. Retrieved 2025-01-25.
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62. ^ Hartl, Michael (2010). "Tau Day – No, really, pi is wrong: The Tau Manifesto". Retrieved 2015-03-20.
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64. ^ Weisstein, Eric W. "Golden Ratio". mathworld.wolfram.com. Retrieved 2025-02-06.
65. ^ Weisstein, Eric W. "Totient Function". mathworld.wolfram.com. Retrieved 2025-02-06.
66. ^ Weisstein, Eric W. "Chromatic Number". mathworld.wolfram.com. Retrieved 2025-02-09. The chromatic number of a graph G is most commonly denoted χ (G) (e.g., Skiena 1990, West 2000, Godsil and Royle 2001, Pemmaraju and Skiena 2003),...
67. ^ Weisstein, Eric W. "Euler Characteristic". mathworld.wolfram.com. Retrieved 2025-02-09.
68. ^ Mugiraneza, Sam; Hallas, Alannah M. (2022-04-19). "Tutorial: a beginner's guide to interpreting magnetic susceptibility data with the Curie-Weiss law". Communications Physics. 5 (1): 95. arXiv:2205.07107. Bibcode:2022CmPhy...5...95M. doi:10.1038/s42005-022-00853-y. ISSN 2399-3650. However, for newly synthesized materials, there is one indispensable characterization technique that is as old as the field of magnetism itself: magnetic susceptibility, χ,...
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70. ^ Weisstein, Eric W. "Reciprocal Fibonacci Constant". mathworld.wolfram.com. Retrieved 2025-02-08.
71. ^ Weisstein, Eric W. "Chebyshev Functions". mathworld.wolfram.com. Retrieved 2025-02-08.
72. ^ Weisstein, Eric W. "Polygamma Function". mathworld.wolfram.com. Retrieved 2025-02-08. A special function mostly commonly denoted ψ_n(z), ψ^((n))(z), or F_n(z-1)...
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75. ^ Rein, Alan (2020-07-28). "The heart of the HIV RNA packaging signal?". Proceedings of the National Academy of Sciences of the United States of America. 117 (33): 19621–19623. Bibcode:2020PNAS..11719621R. doi:10.1073/pnas.2013378117. PMC 7443930. PMID 32723818. vRNA is selectively packaged because it contains a "packaging signal" or "ψ" [also designated the "core encapsidation signal" (2)].
76. ^ WELBAUM, GREGORY E.; BRADFORD, KENT J. (1991-03-01). "Water Relations of Seed Development and Germination in Muskmelon (Cucumis melo L.): VI. INFLUENCE OF PRIMING ON GERMINATION RESPONSES TO TEMPERATURE AND WATER POTENTIAL DURING SEED DEVELOPMENT". Journal of Experimental Botany. 42 (3): 393–399. doi:10.1093/jxb/42.3.393. ISSN 0022-0957. Germination sensitivities to temperature and water potential (ψ) were quantified as indicators of the influence of seed maturity and priming on seed vigour.
77. ^ "Ohm | Electricity, Resistance & Voltage | Britannica". www.britannica.com. 2025-01-03. Retrieved 2025-02-08. ohm, abbreviation Ω, unit of electrical resistance in the metre-kilogram-second system,
78. ^ Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 347. ISBN 978-0-12-373980-3. OCLC 156811865.
79. ^ Weisstein, Eric W. "Omega Constant". mathworld.wolfram.com. Retrieved 2025-02-06.
80. ^ Weisstein, Eric W. "Solid Angle". mathworld.wolfram.com. Retrieved 2025-02-07. The solid angle Ω subtended by a surface S is defined as the surface area Ω of a unit sphere covered by the surface's projection onto the sphere.
81. ^ Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 346. ISBN 978-0-12-373980-3. OCLC 156811865.
82. ^ "Density Parameter | COSMOS". astronomy.swin.edu.au. Retrieved 2025-02-07.
83. ^ Weisstein, Eric W. "Ordinal Number". mathworld.wolfram.com. Retrieved 2025-02-06. The first transfinite ordinal, denoted ω ...
84. ^ Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 346. ISBN 978-0-12-373980-3. OCLC 156811865.
85. ^ Weisstein, Eric W. "Distinct Prime Factors". mathworld.wolfram.com. Retrieved 2025-02-06.
86. ^ Weisstein, Eric W. "Clique". mathworld.wolfram.com. Retrieved 2025-02-07. A clique of a graph G is a complete subgraph of G, and the clique of largest possible size is referred to as a maximum clique (which has size known as the (upper) clique number ω(G)).

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