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{{Redirect-distinguish|Λ|Turned v|ʎ|Radical 11{{!}}入|El (Cyrillic){{!}}Л}}
{{Redirect-distinguish|Λ|Turned v|ʎ|Radical 11{{!}}入|El (Cyrillic){{!}}Л}}
{{Greek Alphabet|letter=lambda}}
{{Greek Alphabet|letter=lambda}}
'''Lambda''' ({{IPAc-en|'|l|{|m|d|@|audio=en-us-lambda.ogg}};<ref>{{OED|lambda}}</ref> uppercase '''{{lang|el|Λ}}''', lowercase '''{{lang|el|λ}}'''; {{langx|el|λάμ(β)δα}}, ''lám(b)da'') is the eleventh letter of the [[Greek alphabet]], representing the [[Dental, alveolar and postalveolar lateral approximants|voiced alveolar lateral approximant]] {{IPA|el|l|IPA}}. In the system of [[Greek numerals]], lambda has a value of 30. Lambda is derived from the [[Phoenician alphabet|Phoenician]] [[Lamed]]. Lambda gave rise to the [[Latin script|Latin]] [[L]] and the [[Cyrillic script|Cyrillic]] [[El (Cyrillic)|El]] (Л). The ancient [[Alexandrine grammarians|grammarians]] and dramatists give evidence to the pronunciation as {{IPA|el|laːbdaː|}} ({{lang|grc|λάβδα}}) in [[Classical Greek]] times.<ref>Herbert Weir Smyth. ''A Greek Grammar for Colleges''. [https://www.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.04.0007 I.1.c]</ref> In [[Modern Greek]], the name of the letter, Λάμδα, is pronounced {{IPA|el|ˈlam.ða|}}.
'''Lambda'''({{IPAc-en|'|l|{|m|d|@|audio=en-us-lambda.ogg}};<ref name="OEDPron">{{OED|lambda|4098469757|subsection=Pronunciation|subid=7055602338}}</ref> uppercase '''{{lang|mul-Grek|Λ}}''', lowercase '''{{lang|mul-Grek|λ}}'''; {{langx|el|λάμ(β)δα}}, {{transliteration|el|lám(b)da}}; {{langx|grc|λά(μ)βδα}}, {{transliteration|grc|lá(m)bda}}), sometimes rendered '''lamda''',<ref name="OEDForms">{{OED|lambda|4098469757|subsection=Forms|subid=1663278936}}</ref> '''labda'''<ref name="OEDForms"/> or '''lamma''',<ref name="OEDForms"/> is the eleventh letter of the [[Greek alphabet]], representing the [[Dental, alveolar and postalveolar lateral approximants|voiced alveolar lateral approximant]] {{IPA|el|l|IPA}}; it derives from the [[Phoenician alphabet|Phoenician]] letter [[Lamed]], and gave rise to [[Latin script|Latin]] [[L]] and [[Cyrillic script|Cyrillic]] [[El (Cyrillic)|El]] ({{lang|mul-Cyrl|Л}}). In the system of [[Greek numerals]], lambda has a value of 30. The ancient [[Alexandrine grammarians|grammarians]] typically called it {{lang|grc|λάβδα}} ({{transliteration|grc|lắbdă}}, {{IPA|grc|lábda|}}) in [[Classical Greek]] times,<ref>Herbert Weir Smyth. ''A Greek Grammar for Colleges''. [https://www.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.04.0007 I.1.c]</ref> whereas in [[Modern Greek]] it is {{lang|el|λάμδα}} ({{transliteration|el|lámda}}, {{IPA|el|ˈlamða|}}), while the spelling {{lang|grc|λάμβδα}} ({{transliteration|el|lámbda}}) was used (to varying degrees) throughout the lengthy transition between the two.


In [[Epichoric alphabets|early Greek alphabets]], the shape and orientation of lambda varied.<ref>{{cite web|url=http://poinikastas.csad.ox.ac.uk/browseGlyphs.shtml|title=Epigraphic Sources for Early Greek Writing|website=Poinikastas.CSAD.ox.ac.uk|access-date=2011-10-03}}</ref> Most variants consisted of two straight strokes, one longer than the other, connected at their ends. The angle might be in the upper-left, lower-left ("Western" alphabets) or top ("Eastern" alphabets). Other variants had a vertical line with a horizontal or sloped stroke running to the right. With the general adoption of the [[History of the Greek alphabet#Standardization – the Ionic alphabet|Ionic alphabet]], Greek settled on an angle at the top; the Romans put the angle at the lower-left.
In [[Epichoric alphabets|early Greek alphabets]], the shape and orientation of lambda varied.<ref>{{cite web|url=http://poinikastas.csad.ox.ac.uk/browseGlyphs.shtml|title=Epigraphic Sources for Early Greek Writing|website=Poinikastas.CSAD.ox.ac.uk|access-date=2011-10-03}}</ref> Most variants consisted of two straight strokes, one longer than the other, connected at their ends. The angle might be in the upper-left, lower-left ("Western" alphabets) or top ("Eastern" alphabets). Other variants had a vertical line with a horizontal or sloped stroke running to the right. With the general adoption of the [[History of the Greek alphabet#Standardization – the Ionic alphabet|Ionic alphabet]], Greek settled on an angle at the top; the Romans put the angle at the lower-left.
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* The [[lambda particle]] is a type of [[subatomic particle]] in [[Physics#High energy/particle physics|subatomic particle physics]].
* The [[lambda particle]] is a type of [[subatomic particle]] in [[Physics#High energy/particle physics|subatomic particle physics]].
* Lambda is the set of logical axioms in the [[axiomatic method]] of logical deduction in [[first-order logic]].
* Lambda is the set of logical axioms in the [[axiomatic method]] of logical deduction in [[first-order logic]].
* Uppercase Lambda is often used as a stylized form of uppercase [[A]], especially in science fiction.
* There is a poetical allusion to the use of Lambda as a [[aspis|shield blazon]] by the [[Spartans]].{{Citation needed|date=March 2022}}<ref>{{cite book |last1=Philodemus |title=On Poems |date=2003 |publisher=Oxford University Press |page=212 |isbn=9780199262854}}</ref>
* There is a poetical allusion to the use of Lambda as a [[aspis|shield blazon]] by the [[Spartans]].{{Citation needed|date=March 2022}}<ref>{{cite book |last1=Philodemus |title=On Poems |date=2003 |publisher=Oxford University Press |page=212 |isbn=9780199262854}}</ref>
* Lambda is the [[von Mangoldt function]] in mathematical [[number theory]].<ref>{{Cite book |last=Deza |first=Elena |title=Perfect and amicable numbers |date=2023 |publisher=World Scientific |isbn=978-981-12-5962-3 |series=Selected chapters of number theory : special numbers |location=New Jersey |pages=79 |quote=The ''von Mangold function'' Λ(''n'') is defined as…}}</ref>
* Lambda is the [[von Mangoldt function]] in mathematical [[number theory]].<ref>{{Cite book |last=Deza |first=Elena |title=Perfect and amicable numbers |date=2023 |publisher=World Scientific |isbn=978-981-12-5962-3 |series=Selected chapters of number theory : special numbers |location=New Jersey |pages=79 |quote=The ''von Mangold function'' Λ(''n'') is defined as…}}</ref>
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Examples of the symbolic use of lowercase lambda include:
Examples of the symbolic use of lowercase lambda include:
* λ indicates the [[wavelength]] of any [[wave]], especially in [[physics]], [[electrical engineering]], and [[mathematics]].<ref>{{Cite book |title=Fundamentals of Physics |last=Nelkon |first=Michael |publisher=Hart-Davis Educational |year=1977 |location=St. Albans, Hertfordshire |pages=329}}</ref>
* λ indicates the [[wavelength]] of any [[wave]], especially in [[physics]], [[electrical engineering]], and [[mathematics]].<ref>{{Cite book |title=Fundamentals of Physics |last=Nelkon |first=Michael |publisher=Hart-Davis Educational |year=1977 |location=St. Albans, Hertfordshire |pages=329}}</ref>
* In [[evolutionary algorithm]]s, λ indicates the number of offspring that would be generated from μ current population in each generation. The terms μ and λ are originated from [[Evolution strategy]] notation.<ref>{{Cite book |last=Baragona |first=Roberto |title=Evolutionary statistical procedures: an evolutionary computation approach to statistical procedures designs and applications |date=2011 |publisher=Springer |others=Francesco Battaglia, Irene Poli |isbn=978-3-642-16217-6 |series=Statistics and computing |location=Berlin |pages=16 |quote=… ,and λ is the number of offsprings at each generation:}}</ref>
* In [[evolutionary algorithm]]s, λ indicates the number of offspring that would be generated from μ current population in each generation. The terms μ and λ are originated from [[evolution strategy]] notation.<ref>{{Cite book |last=Baragona |first=Roberto |title=Evolutionary statistical procedures: an evolutionary computation approach to statistical procedures designs and applications |date=2011 |publisher=Springer |others=Francesco Battaglia, Irene Poli |isbn=978-3-642-16217-6 |series=Statistics and computing |location=Berlin |pages=16 |quote=…, and λ is the number of offsprings at each generation:}}</ref>
* λ indicates the [[exponential decay|radioactivity decay constant]] in [[nuclear physics]] and [[radioactivity]]. This constant is very simply related (by a multiplicative constant) to the [[half-life]] of any radioactive material.
* λ indicates the [[exponential decay|radioactivity decay constant]] in [[nuclear physics]] and [[radioactivity]]. This constant is very simply related (by a multiplicative constant) to the [[half-life]] of any radioactive material.
* In [[probability theory]], λ represents the density of occurrences within a time interval, as modelled by the [[Poisson distribution]].<ref>{{Cite book |last=Panik |first=Michael J. |title=Advanced statistics from an elementary point of view |date=2005 |publisher=Elsevier/Academic Press |isbn=978-0-12-088494-0 |location=Boston |pages=260 |quote=Since λ is the mean number of occurrences per unit time of the Poisson process,}}</ref>
* In [[probability theory]], λ represents the density of occurrences within a time interval, as modelled by the [[Poisson distribution]].<ref>{{Cite book |last=Panik |first=Michael J. |title=Advanced statistics from an elementary point of view |date=2005 |publisher=Elsevier/Academic Press |isbn=978-0-12-088494-0 |location=Boston |pages=260 |quote=Since λ is the mean number of occurrences per unit time of the Poisson process,}}</ref>
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* In the physics of [[electric field]]s, lambda sometimes indicates the linear [[charge density]] of a uniform line of [[electric charge]] (measured in [[coulomb]]s per meter).
* In the physics of [[electric field]]s, lambda sometimes indicates the linear [[charge density]] of a uniform line of [[electric charge]] (measured in [[coulomb]]s per meter).
* Lambda denotes a [[Lagrange multiplier]] in [[multivariable calculus|multi-dimensional calculus]].<ref>{{Cite book |last=Ito |first=Kazufumi |title=Lagrange multiplier approach to variational problems and applications |date=2008 |publisher=Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, Pennsylvania 19104) |others=K. Kunisch, Society for Industrial and Applied Mathematics |isbn=978-0-89871-649-8 |series=Advances in Design and Control |location=Philadelphia, Pa |pages=xii |quote=Here the Lagrange multiplier λ is treated like an independent variable just like ''y'' and ''u''.}}</ref>
* Lambda denotes a [[Lagrange multiplier]] in [[multivariable calculus|multi-dimensional calculus]].<ref>{{Cite book |last=Ito |first=Kazufumi |title=Lagrange multiplier approach to variational problems and applications |date=2008 |publisher=Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, Pennsylvania 19104) |others=K. Kunisch, Society for Industrial and Applied Mathematics |isbn=978-0-89871-649-8 |series=Advances in Design and Control |location=Philadelphia, Pa |pages=xii |quote=Here the Lagrange multiplier λ is treated like an independent variable just like ''y'' and ''u''.}}</ref>
* In [[solid-state electronics]], lambda indicates the [[channel length modulation]] parameter of a [[MOSFET]].<ref>{{Cite book |last=Wiegerink |first=Remco J. |title=Analysis and synthesis of MOS translinear circuits |date=1993 |publisher=Kluwer Academic |isbn=978-0-7923-9390-0 |series=The Kluwer international series in engineering and computer science ; Analog circuits and signal processing |location=Boston |pages=21 |quote=Channel length modulation in an MOS transistor causes the drain current to be dependent on the drain voltage.… and λ the channel-length modulation parameter.}}</ref>
* In [[solid-state electronics]], lambda indicates the [[channel length modulation]] parameter of a [[MOSFET]].<ref>{{Cite book |last=Wiegerink |first=Remco J. |title=Analysis and synthesis of MOS translinear circuits |date=1993 |publisher=Kluwer Academic |isbn=978-0-7923-9390-0 |series=The Kluwer international series in engineering and computer science; Analog circuits and signal processing |location=Boston |pages=21 |quote=Channel length modulation in an MOS transistor causes the drain current to be dependent on the drain voltage.… and λ the channel-length modulation parameter.}}</ref>
* In [[ecology]], lambda denotes the long-term intrinsic growth rate of a population.<ref>{{Cite book |last=Li |first=Xue-Zhi |title=Age Structured Epidemic Modeling |last2=Yang |first2=Junyuan |last3=Martcheva |first3=Maia |date=2020 |publisher=Springer International Publishing AG |isbn=978-3-030-42495-4 |series=Interdisciplinary Applied Mathematics |location=Cham |pages=7 |quote=λ* is called the ''Malthusian parameter'' or ''intrinsic growth rate''.}}</ref> This value is often calculated as the dominant eigenvalue of the age/size class [[matrix (mathematics)|matrix]].
* In [[ecology]], lambda denotes the long-term intrinsic growth rate of a population.<ref>{{Cite book |last=Li |first=Xue-Zhi |title=Age Structured Epidemic Modeling |last2=Yang |first2=Junyuan |last3=Martcheva |first3=Maia |date=2020 |publisher=Springer International Publishing AG |isbn=978-3-030-42495-4 |series=Interdisciplinary Applied Mathematics |location=Cham |pages=7 |quote=λ* is called the ''Malthusian parameter'' or ''intrinsic growth rate''.}}</ref> This value is often calculated as the dominant eigenvalue of the age/size class [[matrix (mathematics)|matrix]].
* In [[formal language theory]] and in computer science, lambda denotes the [[empty string]].<ref>{{Cite book |last=Tourlakis |first=George J. |title=Discrete mathematics: a concise introduction |date=2024 |publisher=Springer |isbn=978-3-031-30487-3 |series=Synthesis lectures on mathematics & statistics |location=Cham |pages=37 |quote=The symbols prevalent in the literature used to denote the empty string are ϵ or λ. We will choose λ…}}</ref>
* In [[formal language theory]] and in computer science, lambda denotes the [[empty string]].<ref>{{Cite book |last=Tourlakis |first=George J. |title=Discrete mathematics: a concise introduction |date=2024 |publisher=Springer |isbn=978-3-031-30487-3 |series=Synthesis lectures on mathematics & statistics |location=Cham |pages=37 |quote=The symbols prevalent in the literature used to denote the empty string are ϵ or λ. We will choose λ…}}</ref>
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* In 1970, a lowercase lambda was chosen by [[Tom Doerr]] as the symbol of the New York chapter of the [[Gay Activists Alliance]].<ref>{{cite web |last=Rapp |first=Linda |title=Gay Activists Alliance |url=http://www.glbtqarchive.com/ssh/gay_activists_alliance_S.pdf |publisher=[[glbtq.com]] |year=2004}}</ref><ref>{{cite web |title=1969, The Year of Gay Liberation |url=http://web-static.nypl.org/exhibitions/1969/ref/1696848.html |publisher=[[The New York Public Library]] |date=June 2009 |access-date=17 November 2018}}</ref> The lambda symbol became associated with [[gay liberation]]<ref>{{cite book |last1=Goodwin |first1=Joseph P. |title=More Man Than You'll Ever Be: Gay Folklore and Acculturation in Middle America |url=https://archive.org/details/moremanthanyoull00good |url-access=registration |date=1989 |publisher=Indiana University Press |page=[https://archive.org/details/moremanthanyoull00good/page/26 26] |chapter=It Takes One to Know One |isbn=978-0253338938}}</ref><ref>{{cite web |last1=Rapp |first1=Linda |title=Symbols |url=http://www.glbtqarchive.com/arts/symbols_A.pdf |publisher=[[glbtq.com]] |date=2003}}</ref> and recognized as an [[LGBTQ symbols|LGBTQ symbol]] for some time afterwards, being used as such by the International Gay Rights Congress in Edinburgh.<ref>{{cite book |editor1-last=Haggerty |editor1-first=George E. |title=Gay Histories and Cultures: An Encyclopedia (Encyclopedia of Gay Histories and Cultures, Volume II) |date=2000 |publisher=Garland Publishing |location=London |page=[https://archive.org/details/encyclopediaofga00ghag/page/529 529] |edition=1 |oclc=750790369 |isbn=0-8153-1880-4 |url-access=registration |url=https://archive.org/details/encyclopediaofga00ghag/page/529 }}</ref>
* In 1970, a lowercase lambda was chosen by [[Tom Doerr]] as the symbol of the New York chapter of the [[Gay Activists Alliance]].<ref>{{cite web |last=Rapp |first=Linda |title=Gay Activists Alliance |url=http://www.glbtqarchive.com/ssh/gay_activists_alliance_S.pdf |publisher=[[glbtq.com]] |year=2004}}</ref><ref>{{cite web |title=1969, The Year of Gay Liberation |url=http://web-static.nypl.org/exhibitions/1969/ref/1696848.html |publisher=[[The New York Public Library]] |date=June 2009 |access-date=17 November 2018}}</ref> The lambda symbol became associated with [[gay liberation]]<ref>{{cite book |last1=Goodwin |first1=Joseph P. |title=More Man Than You'll Ever Be: Gay Folklore and Acculturation in Middle America |url=https://archive.org/details/moremanthanyoull00good |url-access=registration |date=1989 |publisher=Indiana University Press |page=[https://archive.org/details/moremanthanyoull00good/page/26 26] |chapter=It Takes One to Know One |isbn=978-0253338938}}</ref><ref>{{cite web |last1=Rapp |first1=Linda |title=Symbols |url=http://www.glbtqarchive.com/arts/symbols_A.pdf |publisher=[[glbtq.com]] |date=2003}}</ref> and recognized as an [[LGBTQ symbols|LGBTQ symbol]] for some time afterwards, being used as such by the International Gay Rights Congress in Edinburgh.<ref>{{cite book |editor1-last=Haggerty |editor1-first=George E. |title=Gay Histories and Cultures: An Encyclopedia (Encyclopedia of Gay Histories and Cultures, Volume II) |date=2000 |publisher=Garland Publishing |location=London |page=[https://archive.org/details/encyclopediaofga00ghag/page/529 529] |edition=1 |oclc=750790369 |isbn=0-8153-1880-4 |url-access=registration |url=https://archive.org/details/encyclopediaofga00ghag/page/529 }}</ref>
* [[Golomb–Dickman constant]]<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Golomb-Dickman Constant Continued Fraction |url=https://mathworld.wolfram.com/Golomb-DickmanConstantContinuedFraction.html |access-date=2025-01-31 |website=mathworld.wolfram.com |language=en}}</ref>
* [[Golomb–Dickman constant]]<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Golomb-Dickman Constant Continued Fraction |url=https://mathworld.wolfram.com/Golomb-DickmanConstantContinuedFraction.html |access-date=2025-01-31 |website=mathworld.wolfram.com |language=en}}</ref>
* In continuum mechanics, lambda represents one of the [[Lamé parameters]], which is a material property that arises in stress-strain relationships.


===Litra symbol===
===Litra symbol===
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==See also==
==See also==
{{Wiktionary|Λ|λ}}
{{Wiktionary|Λ|λ|Ꟛ|ꟛ}}
* [[Barred lambda]] - ƛ
* [[Barred lambda]] - ƛ
* [[El (Cyrillic)]] – Л, л
* [[El (Cyrillic)]] – Л, л

Latest revision as of 03:30, 13 October 2025

Template:Short description Script error: No such module "about". Template:Redirect-distinguish Template:Greek Alphabet Lambda(Template:IPAc-en;[1] uppercase Script error: No such module "Lang"., lowercase Script error: No such module "Lang".; Template:Langx, Template:Transliteration; Template:Langx, Template:Transliteration), sometimes rendered lamda,[2] labda[2] or lamma,[2] is the eleventh letter of the Greek alphabet, representing the voiced alveolar lateral approximant Script error: No such module "IPA".; it derives from the Phoenician letter Lamed, and gave rise to Latin L and Cyrillic El (Script error: No such module "Lang".). In the system of Greek numerals, lambda has a value of 30. The ancient grammarians typically called it Script error: No such module "Lang". (Template:Transliteration, Script error: No such module "IPA".) in Classical Greek times,[3] whereas in Modern Greek it is Script error: No such module "Lang". (Template:Transliteration, Script error: No such module "IPA".), while the spelling Script error: No such module "Lang". (Template:Transliteration) was used (to varying degrees) throughout the lengthy transition between the two.

In early Greek alphabets, the shape and orientation of lambda varied.[4] Most variants consisted of two straight strokes, one longer than the other, connected at their ends. The angle might be in the upper-left, lower-left ("Western" alphabets) or top ("Eastern" alphabets). Other variants had a vertical line with a horizontal or sloped stroke running to the right. With the general adoption of the Ionic alphabet, Greek settled on an angle at the top; the Romans put the angle at the lower-left.

File:NAMA Alphabet grec.jpg
The Greek alphabet on a black figure vessel, with a Phoenician-lamed-shaped lambda. The gamma has the shape of modern lambda.

Symbol

Upper-case letter Λ

Examples of the symbolic use of uppercase lambda include:

Lower-case letter λ

File:Greek lc lamda thin.svg
Lower-case lambda

Examples of the symbolic use of lowercase lambda include:

Litra symbol

The Roman Script error: No such module "Lang". and Byzantine Script error: No such module "Lang". (Script error: No such module "Lang".), which served as both the pound mass unit and liter volume unit, were abbreviated in Greek using lambda with modified forms of the iota subscript ⟨λͅ⟩. These are variously encoded in Unicode. The Ancient Greek Numbers Unicode block includes 10183 Template:Sc (𐆃) as well as 𐅢, which is described as 10162 Template:Sc[37] but was much more common as a form of the litra sign. A variant of the sign can be formed from 0338 Template:Sc and either 039B Template:Sc (Λ̸) or 03BB Template:Sc (λ̸).[38]

Unicode

Unicode uses the (Modern Greek-based) spelling "lamda" in character names, instead of "lambda", due to "the pre-existing names in ISO 8859-7, as well as preferences expressed by the Greek National Body".[39] Latin versions of lambda were added to Unicode in 2024 for the Salishan and Wakashan languages in Canada.[40]

Template:Notelist

See also

Template:Sister project

References

Template:Reflist

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  1. Template:OED
  2. a b c Template:OED
  3. Herbert Weir Smyth. A Greek Grammar for Colleges. I.1.c
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  28. Wankat Separation Process Engineering 2nd ed, Prentice Hall
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  37. Unicode Ancient Greek Numbers block.
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