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| {{Use British English|date=March 2013}}
| | The name of the author is Figures. She is a librarian but she's usually needed her personal business. Puerto Rico is exactly where he and his wife live. His spouse doesn't like it the way he does but what he truly likes performing is to do aerobics and he's been doing it for fairly a whilst.<br><br>My blog; [http://i4p.info/article.php?id=114136 at home std testing] |
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| {{infobox person
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| | native_name = സംഗമഗ്രാമ മാധവൻ
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| | native_name_lang = ml
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| | name = Madhava
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| | image =
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| | birth_date = {{circa|1340}}<ref name=rajag78/><ref name="Roy1990">{{cite journal| first=Ranjan| last=Roy| year=1990| title=The Discovery of the Series Formula for π by Leibniz, Gregory and Nilakantha| journal=Mathematics Magazine| volume=63| issue=5| pages=291–306| url=http://mathdl.maa.org/images/upload_library/22/Allendoerfer/1991/0025570x.di021167.02p0073q.pdf| format=PDF| doi=10.2307/2690896}}</ref><ref name=Pearce>Ian G. Pearce (2002). [http://www-gap.dcs.st-and.ac.uk/~history/Projects/Pearce/Chapters/Ch9_3.html Madhava of Sangamagramma]. ''[[MacTutor History of Mathematics archive]]''. [[University of St Andrews]].</ref> (or {{c.|1350}}<ref name=mact-biog/>)
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| | death_date = {{circa|1425}}
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| | resting_place_coordinates = <!-- {{coord|LAT|LONG|display=inline,title}} -->
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| | residence = [[Sangamagrama]] ([[Irinjalakuda]]) in [[Kerala]]
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| | nationality = [[India]]n
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| | ethnicity = [[Namputiri]]
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| | citizenship =
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| | other_names =
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| | known_for = Discovery of [[power series]] expansions of trigonometric [[sine]], [[cosine]] and [[arctangent]] functions
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| | education =
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| | alma_mater =
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| | employer =
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| | notable works = Golavada, Madhyamanayanaprakara, [[Venvaroha]]
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| | occupation = [[Astronomer]]-[[mathematician]]
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| | title = ''Golavid''
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| | religion = [[Hinduism]]
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| '''Madhava of Sangamagrama''' ({{circa|1340|1425}}), was an [[Indian mathematician]]-[[Indian astronomy|astronomer]] from the town of [[Sangamagrama]] (present day [[Irinjalakuda]]) near [[Thrissur]], Kerala, India. He is considered the founder of the [[Kerala school of astronomy and mathematics]]. He was the first in the world to use [[Series (mathematics)|infinite series]] approximations for a range of trigonometric functions, which has been called the "decisive step onward from the finite procedures of ancient mathematics to treat their [[Limit (mathematics)|limit]]-passage to [[infinity]]".<ref name=rajag78>
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| {{cite journal
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| | title = On an untapped source of medieval Keralese Mathematics
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| | author = C. T. Rajagopal and M. S. Rangachari
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| | journal = Archive for History of Exact Sciences
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| | url = http://www.springerlink.com/content/mnr38341u762u544/?p=a9e26ffde91946b288bcb6deebac245c&pi=0
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| | volume = 18 | number=2
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| |date=June 1978
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| | pages = 89–102
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| }}</ref> His discoveries opened the doors to what has today come to be known as [[Mathematical Analysis]].<ref name=mact-biog>{{cite web
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| | publisher=School of Mathematics and Statistics, [[University of St Andrews]], Scotland | title=Madhava of Sangamagramma
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| |author = J J O'Connor and E F Robertson | year=2000
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| |url=http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Madhava.html
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| | work=[[MacTutor History of Mathematics archive]]
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| | accessdate=2007-09-08
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| }}
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| </ref> One of the greatest mathematician-astronomers of the [[Middle Ages]], Madhava made pioneering contributions to the study of infinite series, [[calculus]], [[trigonometry]], [[geometry]], and [[algebra]].
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| Some scholars have also suggested that Madhava's work, through the writings of the Kerala school, may have been transmitted to Europe via [[Jesuit]] missionaries and traders who were active around the ancient port of [[Muziris]] at the time. As a result, it may have had an influence on later European developments in analysis and calculus.<ref name=almeida>{{cite journal
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| |author = D F Almeida, J K John and A Zadorozhnyy
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| |title = Keralese mathematics: its possible transmission to Europe and the consequential educational implications
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| | journal = Journal of Natural Geometry
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| |volume= 20
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| |year =2001
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| |pages=77–104
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| |issue=1
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| }}</ref>
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| ==Name==
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| Madhava was born as ''Irińńaŗappiļļy or Iriññinavaļļi Mādhava Namboodiri.'' He had written that his house name was related to the Vihar where a plant called "bakuļam" was planted. According to [[Achyuta Pisharati]], (who wrote a commentary on [[Venvaroha|Veņwarõham]] written by Madhava) ''bakuļam'' was locally known as "iraňňi". Dr. K.V. Sarma, an authority on Madhava has the opinion that the house name is either Irińńāŗappiļļy or Iriññinavaļļy'.
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| Irinjalakuda was once known as 'Irińńāţikuţal'. [[Sangamagrama|Sangamagrāmam]] (lit. ''sangamam'' = union, ''grāmam'' = village) is a rough translation to Sanskrit from Dravidian word 'Irińńāţikuţal', which means 'iru (two) ańńāţi (market) kǖţal (union)' or the union of two markets.
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| ==Historiography==
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| Although there is some evidence of mathematical work in Kerala prior to Madhava (''e.g.'', ''[[Sadratnamala]]'' c. 1300, a set of fragmentary results<ref name=whish/>), it is clear from citations that Madhava provided the creative impulse for the development of a rich mathematical tradition in medieval Kerala. However, most of Madhava's original work (except a couple of them) is lost. He is referred to in the work of subsequent Kerala mathematicians, particularly in [[Nilakantha Somayaji]]'s ''Tantrasangraha'' (c. 1500), as the source for several infinite series expansions, including sin''θ'' and arctan''θ''. The 16th-century text ''Mahajyānayana prakāra'' cites Madhava as the source for several series derivations for π. In [[Jyeṣṭhadeva]]'s ''[[Yuktibhāṣā]]'' (c. 1530),<ref name=sarma>
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| {{cite web
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| | editor=[[K. V. Sarma]] & S Hariharan
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| | work=Yuktibhāṣā of Jyeṣṭhadeva
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| |url=http://www.new.dli.ernet.in/insa/INSA_1/20005ac0_185.pdf
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| | title=A book on rationales in Indian Mathematics and Astronomy—An analytic appraisal
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| | accessdate=2006-07-09
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| |format=PDF |archiveurl = http://web.archive.org/web/20060928203221/http://www.new.dli.ernet.in/insa/INSA_1/20005ac0_185.pdf <!-- Bot retrieved archive --> |archivedate = 28 September 2006}}
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| </ref> written in [[Malayalam language|Malayalam]], these series are presented with proofs in terms of the [[Taylor series]] expansions for polynomials like 1/(1+''x''<sup>2</sup>), with ''x'' = tan''θ'', etc.
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| Thus, what is explicitly Madhava's work is a source of some debate. The ''Yukti-dipika'' (also called the ''Tantrasangraha-vyakhya''), possibly composed [[Sankara Variyar]], a student of Jyeṣṭhadeva, presents several versions of the series expansions for sin''θ'', cos''θ'', and arctan''θ'', as well as some products with radius and arclength, most versions of which appear in Yuktibhāṣā. For those that do not, Rajagopal and Rangachari have argued, quoting extensively from the original Sanskrit,<ref name=rajag78/> that since some of these have been attributed by Nilakantha to Madhava, possibly some of the other forms might also be the work of Madhava.
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| Others have speculated that the early text ''[[Karanapaddhati]]'' (c. 1375–1475), or the ''Mahajyānayana prakāra'' might have been written by Madhava, but this is unlikely.<ref name=Pearce/>
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| ''Karanapaddhati'', along with the even earlier Keralese mathematics text ''Sadratnamala'', as well as the ''Tantrasangraha'' and ''Yuktibhāṣā'', were considered in an 1834 article by [[C.M. Whish|Charles Matthew Whish]], which was the first to draw attention to their priority over Newton in discovering the [[Method of Fluxions|Fluxion]] (Newton's name for differentials).<ref name=whish>{{Cite journal
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| | author = Charles Whish
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| | year = 1834
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| | title = On the [[Hindu]] [[Quadrature of the circle]] and the [[infinite series]] of the proportion of the circumference to the diameter exhibited in the four [[Sastra]]s, the [[Tantrasangraha|Tantra Sahgraham]], Yucti Bhasha, Carana Padhati and Sadratnamala
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| | journal = Transactions of the Royal Asiatic Society of Great Britain and Ireland
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| | publisher = [[Royal Asiatic Society of Great Britain and Ireland]]
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| | doi = 10.1017/S0950473700001221
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| | volume = 3
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| | issue = 3
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| | pages = 509–523
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| | jstor = 25581775
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| | postscript = <!--None-->
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| }}
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| </ref> In the mid-20th century, the Russian scholar Jushkevich revisited the legacy of Madhava,<ref>{{cite book
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| | title = ''Geschichte der Mathematik im Mittelalter'' (German translation, Leipzig, 1964, of the Russian original, Moscow, 1961).
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| | author = A.P. Jushkevich,
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| | year = 1961
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| | place = Moscow
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| }}</ref> and a comprehensive look at the Kerala school was provided by Sarma in 1972.<ref name=sarma>{{cite book
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| | title = A History of the Kerala School of Hindu Astronomy
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| | author = [[K V Sarma]]
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| | year = 1972
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| | address = Hoshiarpur
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| }}</ref>
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| === Lineage ===
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| [[Image:Yuktibhasa.gif|200px|thumb|Explanation of the [[Law of sines|sine rule]] in ''[[Yuktibhāṣā]]'']]
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| There are several known astronomers who preceded Madhava, including Kǖţalur Kizhār (2nd century),<ref>Purananuru 229</ref> Vararuci (4th century), Sankaranarayana (866 AD). It is possible that other unknown figures may have preceded him. However, we have a clearer record of the tradition after Madhava. [[Parameshvara Namboodri]] was a direct disciple. According to a palmleaf manuscript of a Malayalam commentary on the [[Surya Siddhanta]], Parameswara's son Damodara (c. 1400–1500) had both Nilakantha Somayaji as his disciples. Jyeshtadevan was the disciple of Nilakanda. [[Achyuta Pisharati]] of
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| Trikkantiyur is mentioned as a disciple of Jyeṣṭhadeva, and the grammarian [[Melpathur Narayana Bhattathiri]] as his disciple.<ref name=sarma/>
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| ==Contributions==
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| If we consider mathematics as a progression from finite processes of algebra to considerations of the infinite, then the first steps towards this transition typically come with infinite series expansions. It is this transition to the infinite series that is attributed to Madhava. In Europe, the first such series were developed by [[James Gregory (mathematician)|James Gregory]] in 1667. Madhava's work is notable for the series, but what is truly remarkable is his estimate of an error term (or correction term).<ref name=rajag86>Madhava extended Archimedes' work on the geometric Method of Exhaustion to measure areas and numbers such as π, with arbitrary accuracy and error ''limits'', to an algebraic infinite series with a completely separate error ''term''.
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| {{cite journal
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| | title = On medieval Keralese mathematics,
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| | author = C T Rajagopal and M S Rangachari
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| | journal = Archive for History of Exact Sciences
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| | url = http://www.springerlink.com/content/t1343xktl7g52003/
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| | volume = 35
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| | year = 1986
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| | pages = 91–99
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| | doi = 10.1007/BF00357622
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| }}</ref> This implies that the limit nature of the infinite series was quite well understood by him. Thus, Madhava may have invented the ideas underlying [[infinite series]] expansions of functions, [[power series]], [[trigonometric series]], and rational approximations of infinite series.<ref name="MAT 314"/>
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| However, as stated above, which results are precisely Madhava's and which are those of his successors, are somewhat difficult to determine. The following presents a summary of results that have been attributed to Madhava by various scholars.
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| ===Infinite series===
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| ''Main article'' : [[Madhava series]]
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| Among his many contributions, he discovered the infinite series for the [[trigonometric function]]s of [[sine]], [[cosine]], [[tangent (trigonometric function)|tangent]] and [[arctangent]], and many methods for calculating the [[circumference]] of a [[circle]]. One of Madhava's series is known from the text ''[[Yuktibhāṣā]]'', which contains the derivation and proof of the [[power series]] for [[Inverse trigonometric function|inverse tangent]], discovered by Madhava.<ref name="infinity">{{cite web
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| | publisher=D.P. Agrawal—Infinity Foundation |
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| work=Indian Mathemematics
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| |url=http://www.infinityfoundation.com/mandala/t_es/t_es_agraw_kerala.htm
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| | title=The Kerala School, European Mathematics and Navigation
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| | accessdate=2006-07-09
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| }}
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| </ref> In the text, [[Jyeṣṭhadeva]] describes the series in the following manner:
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| {{cquote|The first term is the product of the given sine and radius of the desired arc divided by the cosine of the arc. The succeeding terms are obtained by a process of iteration when the first term is repeatedly multiplied by the square of the sine and divided by the square of the cosine. All the terms are then divided by the odd numbers 1, 3, 5, .... The arc is obtained by adding and subtracting respectively the terms of odd rank and those of even rank. It is laid down that the sine of the arc or that of its complement whichever is the smaller should be taken here as the given sine. Otherwise the terms obtained by this above iteration will not tend to the vanishing magnitude.<ref name=Gupta>
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| {{cite journal
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| | author = R C Gupta
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| | title = The Madhava-Gregory series
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| | journal = Math. Education
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| | volume = 7
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| | year = 1973
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| | pages = B67–B70
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| }}</ref>}}
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| This yields:
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| :<math> r\theta={\frac {r\sin \theta }{\cos \theta
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| }}-(1/3)\,r\,{\frac { \left(\sin \theta \right) ^
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| {3}}{ \left(\cos \theta \right) ^{3}}}+(1/5)\,r\,{\frac {
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| \left(\sin \theta \right) ^{5}}{ \left(\cos
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| \theta \right) ^{5}}}-(1/7)\,r\,{\frac { \left(\sin \theta
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| \right) ^{7}}{ \left(\cos \theta \right) ^{
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| 7}}} + \cdots</math>
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| or equivalently:
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| :<math>\theta = \tan \theta - \frac{\tan^3 \theta}{3} + \frac{\tan^5 \theta}{5} - \frac{\tan^7 \theta}{7} + \cdots</math>
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| This series was traditionally known as the Gregory series (after [[James Gregory (astronomer and mathematician)|James Gregory]], who discovered it three centuries after Madhava). Even if we consider this particular series as the work of [[Jyeṣṭhadeva]], it would pre-date Gregory by a century, and certainly other infinite series of a similar nature had been worked out by Madhava. Today, it is referred to as the Madhava-Gregory-Leibniz series.<ref name=Gupta/><ref name=nair>{{cite web
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| | publisher=Prof. C.G.Ramachandran Nair |
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| work=Government of Kerala—Kerala Call, September 2004
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| |url=http://www.kerala.gov.in/keralcallsep04/p22-24.pdf
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| | title=Science and technology in free India
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| | accessdate=2006-07-09
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| |format=PDF}}
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| </ref>
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| ===Trigonometry===
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| Madhava also gave a most accurate table of sines, defined in terms of the values of the half-sine chords for twenty-four arcs drawn at equal intervals in a quarter of a given circle. It is believed that he may have found these highly accurate tables based on these series expansions:<ref name=mact-biog/>
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| : sin q = q – q<sup>3</sup>/3! + q<sup>5</sup>/5! – ...
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| : cos q = 1 – q<sup>2</sup>/2! + q<sup>4</sup>/4! – ...
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| ===The value of π (pi)===
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| Madhava's work on the value of π is cited in the ''Mahajyānayana prakāra'' ("Methods for the great sines").{{citation needed|date=September 2012}} While some scholars such as Sarma<ref name=sarma/> feel that this book may have been composed by Madhava himself, it is more likely the work of a 16th-century successor.<ref name=mact-biog/> This text attributes most of the expansions to Madhava, and gives
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| the following [[Series (mathematics)|infinite series]] expansion of [[Pi|π]], now known as the [[Leibniz formula for pi|Madhava-Leibniz series]]:<ref>{{Cite book|title=Special Functions|last=George E. Andrews, Richard Askey|first=Ranjan Roy|publisher=[[Cambridge University Press]]|year=1999|isbn=0-521-78988-5|page=58}}</ref><ref>{{Cite journal|first=R. C.|last=Gupta|title=On the remainder term in the Madhava-Leibniz's series|journal=Ganita Bharati|volume=14|issue=1–4|year=1992|pages=68–71}}</ref>
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| :<math>\frac{\pi}{4} = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots + \frac{(-1)^n}{2n + 1} + \cdots</math>
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| which he obtained from the power series expansion of the arc-tangent function. However, what is most impressive is that he also gave a correction term, ''R<sub>n</sub>'', for the error after computing the sum up to ''n'' terms.
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| Madhava gave three forms of ''R<sub>n</sub>'' which improved the approximation,<ref name=mact-biog/> namely
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| : R<sub>n</sub> = 1/(4n), or
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| : R<sub>n</sub> = n/ (4n<sup>2</sup> + 1), or
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| : R<sub>n</sub> = (n<sup>2</sup> + 1) / (4n<sup>3</sup> + 5n).
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| where the third correction leads to highly accurate computations of π.
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| It is not clear how Madhava might have found these correction terms.<ref>T. Hayashi, T. Kusuba and M. Yano. 'The correction of the Madhava series for the circumference of a circle', ''[[Centaurus (journal)|Centaurus]]'' '''33''' (pages 149–174). 1990.</ref> The most convincing is that they come as the first three convergents of a continued fraction which can itself be derived from the standard Indian approximation to π namely 62832/20000 (for the original 5th-century computation, see [[Aryabhata]]).
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| He also gave a more rapidly converging series by transforming the original infinite series of π, obtaining the infinite series
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| :<math>\pi = \sqrt{12}\left(1-{1\over 3\cdot3}+{1\over5\cdot 3^2}-{1\over7\cdot 3^3}+\cdots\right)</math>
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| By using the first 21 terms to compute an approximation of π, he obtains a value correct to 11 decimal places (3.14159265359).<ref name=gupta-pi>
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| {{cite journal
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| | author = R C Gupta
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| | title = Madhava's and other medieval Indian values of pi
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| | journal = Math. Education
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| | volume = 9 (3)
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| | year = 1975
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| | pages = B45–B48
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| }}</ref>
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| The value of
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| 3.1415926535898, correct to 13 decimals, is sometimes attributed to Madhava,<ref>The 13-digit accurate value of π, 3.1415926535898, can be reached using the infinite series expansion of π/4 (the first sequence) by going up to n = 76</ref>
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| but may be due to one of his followers. These were the most accurate approximations of π given since the 5th century (see [[History of numerical approximations of π]]).
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| The text ''Sadratnamala'', usually considered as prior to Madhava, appears to give the astonishingly accurate value of π =3.14159265358979324 (correct to 17 decimal places). Based on this, R. Gupta has argued that this text may also have been composed by Madhava.<ref name=Pearce/><ref name=gupta-pi/>
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| ===Algebra===
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| Madhava also carried out investigations into other series for arclengths and the associated approximations to rational fractions of π, found methods of [[polynomial expansion]], discovered [[Integral test for convergence|tests of convergence]] of infinite series, and the analysis of infinite [[continued fraction]]s.<ref name=Pearce>Ian G. Pearce (2002). [http://www-gap.dcs.st-and.ac.uk/~history/Projects/Pearce/Chapters/Ch9_3.html Madhava of Sangamagramma]. ''[[MacTutor History of Mathematics archive]]''. [[University of St Andrews]].</ref>
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| He also discovered the solutions of [[Transcendental function|transcendental equations]] by [[iteration]], and found the approximation of [[transcendental number]]s by continued fractions.<ref name=Pearce/>
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| ===Calculus===
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| Madhava laid the foundations for the development of [[calculus]], which were further developed by his successors at the [[Kerala school of astronomy and mathematics]].<ref name="MAT 314">{{cite web
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| | publisher=Canisius College |
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| work=MAT 314
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| |url=http://www.canisius.edu/topos/rajeev.asp
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| | title=Neither Newton nor Leibniz – The Pre-History of Calculus and Celestial Mechanics in Medieval Kerala
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| | accessdate=2006-07-09
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| }}
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| </ref><ref name="scotlnd">{{cite web
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| | publisher=School of Mathematics and Statistics University of St Andrews, Scotland |
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| work=Indian Maths
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| |url=http://www-history.mcs.st-andrews.ac.uk/HistTopics/Indian_mathematics.html
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| | title=An overview of Indian mathematics
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| | accessdate=2006-07-07
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| }}
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| </ref> (It should be noted that certain ideas of calculus were known to [[History of calculus|earlier mathematicians]].) Madhava also extended some results found in earlier works, including those of [[Bhāskara II]].
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| Madhava developed some components of [[calculus]] such as [[derivative|differentiation]], term-by-term [[Integral|integration]], [[iterative method]]s for solutions of [[Nonlinearity|non-linear]] equations, and the theory that the area under a curve is its integral.
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| ==Madhava's works==
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| [[K.V. Sarma]] has identified Madhava as the author of the following works:<ref>{{cite book|last=Sarma|first=K.V.|title=Contributions to the study of Kerala school of Hindu astronomy and mathematics|publisher=V V R I|location=Hoshiarpur|year=1977}}</ref><ref>{{cite book|last=David Edwin Pingree|title=Census of the exact sciences in Sanskrit,|publisher=American Philosophical Society|location=Philadelphia|year=1981|series=A|volume=4|pages=414–415}}</ref>
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| #''Golavada''
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| #''Madhyamanayanaprakara''
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| #''Mahajyanayanaprakara''
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| #''Lagnaprakarana'' (लग्नप्रकरण)
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| #''[[Venvaroha]]'' (वेण्वारोह)<ref>{{cite journal|last=K Chandra Hari|year=2003|title=Computation of the true moon by Madhva of Sangamagrama|journal=Indian Journal of History of Science|volume=38|issue=3|pages=231–253|url=http://www.scribd.com/doc/14648892/Venvaroha-Computation-of-Moon-Madhava-of-a|accessdate=27 January 2010}}</ref>
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| #''Sphutacandrapti'' (स्फुटचन्द्राप्ति)
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| #''Aganita-grahacara'' (अगणित-ग्रहचार)
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| #''[[Chandravakyas|Chandravakyani]]'' (चन्द्रवाक्यानि)
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| ==Kerala School of Astronomy and Mathematics==
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| {{Main|Kerala school of astronomy and mathematics}}
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| The Kerala school of astronomy and mathematics flourished for at least two centuries beyond Madhava. In Jyeṣṭhadeva we find the notion of integration, termed ''sankalitam'', (lit. collection), as in the statement:
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| :''ekadyekothara pada sankalitam samam padavargathinte pakuti'',<ref name=nair/>
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| which translates as the integration a variable (''pada'') equals half that
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| variable squared (''varga''); i.e. The integral of x dx is equal to
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| x<sup>2</sup> / 2. This is clearly a start to the process of [[integral calculus]].
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| A related result states that the area under a curve is its [[integral]]. Most of these results pre-date similar results in Europe by several centuries.
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| In many senses,
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| Jyeshthadeva's ''[[Yuktibhāṣā]]'' may be considered the world's first [[calculus]] text.<ref name=whish/><ref name="MAT 314"/><ref name="scotlnd"/>
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| The group also did much other work in astronomy; indeed many more pages are developed to astronomical computations than are for discussing analysis related results.<ref name=sarma/>
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| The Kerala school also contributed much to linguistics (the relation between language and mathematics is an ancient Indian tradition, see [[Katyayana]]). The [[Ayurveda|ayurvedic]] and poetic traditions of [[Kerala]] can also be traced back to this school. The famous poem, [[Narayaneeyam]], was composed by [[Melpathur Narayana Bhattathiri|Narayana Bhattathiri]].
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| ==Influence==
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| Madhava has been called "the greatest mathematician-astronomer of medieval India",<ref name=Pearce/> or as
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| "the founder of mathematical analysis; some of his discoveries in this field show him to have possessed extraordinary intuition."<ref name=jos>{{Cite book|last=Joseph|first=George Gheverghese|origyear=1991|date=October 2010|title=The Crest of the Peacock: Non-European Roots of Mathematics|edition=3rd|publisher=Princeton University Press|isbn=978-0-691-13526-7|url=http://press.princeton.edu/titles/9308.html}}</ref> O'Connor and Robertson state that a fair assessment of Madhava is that
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| he took the decisive step towards modern classical analysis.<ref name=mact-biog/>
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| ===Possible propagation to Europe===
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| The Kerala school was well known in the 15th and 16th centuries, in the period of the first contact with European navigators in the [[Malabar Coast]]. At the time, the port of [[Muziris]], near [[Sangamagrama]], was a major center for maritime trade, and a number of [[Jesuit]] missionaries and traders were active in this region. Given the fame of the Kerala school, and the interest shown by some of the Jesuit groups during this period in local scholarship, some scholars, including G. Joseph of the U. Manchester have suggested<ref name=predated>
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| {{cite news
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| | title = Indians predated Newton 'discovery' by 250 years
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| | publisher = press release, University of Manchester
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| | url = http://www.humanities.manchester.ac.uk/aboutus/news/display/?id=121685
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| | date = 13 August 2007
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| | accessdate = 2007-09-05
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| }}</ref> that the writings of the Kerala school may have also been transmitted to Europe around this time, which was still about a century before Newton.<ref name=almeida/>
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| ==See also==
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| *[[Madhava's sine table]]
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| *[[Madhava series]]
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| *[[Venvaroha]]
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| *[[Indian mathematics]]
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| *[[List of Indian mathematicians]]
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| *[[Kerala school of astronomy and mathematics]]
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| *[[History of calculus]]
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| *[[Ganita-yukti-bhasa]]
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| ==References==
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| {{reflist|2}}
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| {{Indian mathematics}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Madhava of Sangamagrama
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = Indian mathematician
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| | DATE OF BIRTH =
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| | PLACE OF BIRTH =
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| | DATE OF DEATH =
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| }}
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| {{DEFAULTSORT:Madhava Of Sangamagrama}}
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| [[Category:Indian mathematicians]]
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| [[Category:14th-century births]]
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| [[Category:15th-century deaths]]
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| [[Category:14th-century mathematicians]]
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| [[Category:15th-century mathematicians]]
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| [[Category:Medieval Kerala]]
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| [[Category:History of calculus]]
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| [[Category:Indian Hindus]]
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| [[Category:Kerala school]]
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| [[Category:14th-century Indian people]]
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| [[Category:15th-century Indian people]]
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