Kappa

{{Other uses}}{{Distinguish}}{{About|the Greek letter|the archaic Greek letter with a similar name|Koppa (letter)}}{{Distinguish|text=the similar looking Cyrillic letter Ka}}

File:Greek lowercase kappa variant.svg

File:Greek word καί written with a handwritten variant of kappa, from the Byzantine period.png

Kappa ({{IPAc-en|'|k|æ|p|ə|audio=LL-Q1860 (eng)-Flame, not lame-Kappa.wav}};{{OED|kappa}} uppercase Κ, lowercase κ or cursive {{not a typo|ϰ}}; {{langx|el|κάππα}}, káppa) is the tenth letter of the Greek alphabet, representing the voiceless velar plosive {{IPA|el|k|IPA}} sound in Ancient and Modern Greek. In the system of Greek numerals, {{lang|el|Kʹ}} has a value of 20. It was derived from the Phoenician letter kaph 20px. Letters that arose from kappa include the Roman K and Cyrillic К. The uppercase form is identical to the Latin K.

Greek proper names and placenames containing kappa are often written in English with "c" due to the Romans' transliterations into the Latin alphabet: Constantinople, Corinth, Crete. All formal modern romanizations of Greek now use the letter "k", however.{{citation needed|date=February 2018}}

{{anchor|Cursive kappa|{{not a typo|ϰ}}}}

The cursive form {{lang|grc|{{not a typo|ϰ}}}} is generally a simple font variant of lower-case kappa, but it is encoded separately in Unicode for occasions where it is used as a separate symbol in math and science. In mathematics, the kappa curve is named after this letter; the tangents of this curve were first calculated by Isaac Barrow in the 17th century.

Symbol

=Lowercase (κ)=

;Mathematics and statistics

In graph theory, the connectivity of a graph is given by κ.{{Cite web |last=Weisstein |first=Eric W. |title=Vertex Connectivity |url=https://mathworld.wolfram.com/VertexConnectivity.html |access-date=2025-02-05 |website=mathworld.wolfram.com |language=en}}
In differential geometry, the curvature of a curve is given by κ.{{Cite web |last=Weisstein |first=Eric W. |title=Curvature |url=https://mathworld.wolfram.com/Curvature.html |access-date=2025-02-05 |website=mathworld.wolfram.com |language=en |quote=Then the curvature κ, sometimes also called the "first curvature" (Kreyszig 1991, p. 47), is defined by...}}
In linear algebra, the condition number of a matrix is given by κ.{{Cite web |title=DLMF: §3.2 Linear Algebra ‣ Areas ‣ Chapter 3 Numerical Methods |url=https://dlmf.nist.gov/3.2#v.p1 |access-date=2025-01-31 |website=dlmf.nist.gov}}
The kappa curve, also known as Gutschoven's curve, is a curve whose shape resembles the letter κ.{{Cite web |last=Weisstein |first=Eric W. |title=Kappa Curve |url=https://mathworld.wolfram.com/KappaCurve.html |access-date=2025-02-05 |website=mathworld.wolfram.com |language=en}}
Kappa statistics such as Cohen's kappa{{cite journal|last1=McHugh|first1=Mary L.|year=2012|title=Interrater reliability: The kappa statistic|journal=Biochemia Medica|volume=22|issue=3|pages=276–282|doi=10.11613/bm.2012.031|pmc=3900052|pmid=23092060}}{{Cite book |last=Gwet |first=Kilem Li |title=Handbook of inter-rater reliability: the definitive guide to measuring the extent of agreement among raters |date=2014 |publisher=Advances Analytics, LLC |isbn=978-0-9708062-8-4 |edition=Fourth |location=Gaithersburg, Md |pages=32 |quote=Cohen's Kappa Definition}} and Fleiss' kappa are methods for calculating inter-rater reliability.

;Physics

In cosmology, the Einstein gravitational constant is denoted by κ.{{Cite book |last=Carmeli |first=Moshe |title=Classical fields: general relativity and gauge theory |date=1982 |publisher=J. Wiley |isbn=978-0-471-86437-0 |location=New York |pages=85 |quote=Here κ is some constant called Einstein's gravitational constant.}}
In physics, the torsional constant of an oscillator is given by κ.{{Cite book |last=Halliday |first=David |title=Principles of physics |last2=Resnick |first2=Robert |last3=Walker |first3=Jearl |date=2023 |publisher=Wiley |isbn=978-1-119-82061-1 |edition=Twelfth |series=International adaptation |location=Singapore |pages=447 |quote=Here κ (Greek kappa) is a constant, called the torsion constant,}}
In physics, the coupling coefficient in magnetostatics is represented by κ.{{Cite book |last=Stancil |first=Daniel D. |title=Theory of magnetostatic waves |date=1993 |publisher=Springer-Verlag |isbn=978-0-387-97969-4 |location=New York |pages=200 |quote=The coupling coefficient (7.136) can now be written κ{{sub|ab}} =...}}
In physics, the dielectric coefficient is represented by κ.
In fluid dynamics, the von Kármán constant is represented by κ.{{Cite journal |last=Monkewitz |first=Peter A. |last2=Nagib |first2=Hassan M. |date=2023 |title=The hunt for the Kármán ‘constant’ revisited |url=https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/hunt-for-the-karman-constant-revisited/F9DA84F93A1E268BFC5F9E1CB5622E5E |journal=Journal of Fluid Mechanics |language=en |volume=967 |pages=A15 |doi=10.1017/jfm.2023.448 |issn=0022-1120|arxiv=2303.08071 }}
thermal conductivity{{Cite web |title=Thermal Conductivity - Definition and Detailed Explanation |url=https://byjus.com/chemistry/thermal-conductivity/ |access-date=2025-02-05 |website=BYJUS |language=en |quote=It is generally denoted by the symbol ‘k’ but can also be denoted by ‘λ’ and ‘κ’.}}
In thermodynamics, the compressibility of a compound is given by κ.{{Cite book |title=Transition metal and rare earth compounds. 3 |date=2004 |publisher=Springer |isbn=978-3-540-20948-5 |series=Topics in current chemistry |location=Berlin Heidelberg |pages=5 |quote=The isothermal compressibility, κ ...}}

;Engineering

In structural engineering, κ is the ratio of the smaller factored moment to the larger factored moment and is used to calculate the critical elastic moment of an unbraced steel member.
In electrical engineering, κ is the multiplication factor, a function of the R/X ratio of the equivalent power system network, which is used in calculating the peak short-circuit current of a system fault. κ is also used to denote conductivity, the reciprocal of resistivity, rho.

;Biology and biomedical science

In biology, kappa and kappa prime are important nucleotide motifs for a tertiary interaction of group II introns.
In biology, kappa designates a subtype of an antibody component.
In pharmacology, kappa represents a type of opioid receptor.{{Cite book |title=Opioids and Their Receptors: Present and Emerging Concepts in Opioid Drug Discovery II |date=2022 |publisher=MDPI - Multidisciplinary Digital Publishing Institute |isbn=978-3-0365-4352-9 |editor-last=Spetea |editor-first=Mariana |location=Basel |quote=From a chemical standpoint, opioids comprise a diverse group of drugs, but they all share a common affinity towards μ,δ, and κ receptors |editor-last2=van Rijn |editor-first2=Richard M.}}

;Psychology and psychiatry

In psychology and psychiatry, kappa represents a measure of diagnostic reliability.{{Cite book |last=Sadler |first=John Z. |title=Values and psychiatric diagnosis |date=2005 |publisher=Oxford University Press |isbn=978-0-19-852637-7 |series=International perspectives in philosophy and psychiatry |location=Oxford New York, NY |pages=118 |quote=...the other (4b) involve the new (to psychiatry) use of the kappa statistic as a means of measuring diagnostic reliability.}}

;Economics

In macroeconomics, kappa represents the capital-utilization rate.{{Cite web|title=University of Hong Kong School of Business|url=http://www.sef.hku.hk/tpg/econ6022b/lecture_note_6_revised.pdf|website=HKU}}

=Uppercase (Κ)=

;History

In textual criticism, the Byzantine text-type (from Κοινη, Koine, the common text).

;Mathematics and statistics

In set theory, kappa is often used to denote an ordinal that is also a cardinal.

;Chemistry

In chemistry, kappa is used to denote the denticity of the compound.{{Cite book |last=Strohfeldt |first=Katja A. |title=Essentials of Inorganic Chemistry: For Students of Pharmacy, Pharmaceutical Sciences and Medicinal Chemistry |date=2015 |publisher=John Wiley & Sons, Incorporated |isbn=978-0-470-66558-9 |location=Newark |pages=251 |quote=In terms of the nomenclature, the denticity of the ligand is denoted by the Greek letter κ (kappa)}}
In pulping, the kappa number represents the amount of an oxidizing agent required for bleaching a pulp.

Unicode

{{unichar|039A|html=}}
{{unichar|03BA|html=}}
{{unichar|03F0|html=}}
{{unichar|2C94|html=}}
{{unichar|2C95|html=}}
{{unichar|2CB8|html=}}
{{unichar|2CB9|html=}}
{{unichar|1D6B1|html=}}{{efn|The {{sc|mathematical}} symbols are only used for math. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.}}
{{unichar|1D6CB|html=}}
{{unichar|1D6DE|html=}}
{{unichar|1D6EB|html=}}
{{unichar|1D705|html=}}
{{unichar|1D718|html=}}
{{unichar|1D725|html=}}
{{unichar|1D73F|html=}}
{{unichar|1D752|html=}}
{{unichar|1D75F|html=}}
{{unichar|1D779|html=}}
{{unichar|1D78C|html=}}
{{unichar|1D799|html=}}
{{unichar|1D7B3|html=}}
{{unichar|1D7C6|html=}}

References

Category:Greek letters