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Topic: Madhava of Sangamagrama

	Madhava biography
		Madhava of Sangamagramma was born near Cochin on the coast in the Kerala state in southwestern India.
		Madhava discovered the series equivalent to the Maclaurin expansions of sin x, cos x, and arctan x around 1400, which is over two hundred years before they were rediscovered in Europe.
		Madhava also gave a table of almost accurate values of half-sine chords for twenty-four arcs drawn at equal intervals in a quarter of a given circle.
	www-history.mcs.st-andrews.ac.uk /Biographies/Madhava.html (894 words)

	Melpathur Narayana Bhattathiri
		One of Madhava's series is known from the text Yuktibhasa which describes - 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.
		Madhava of Sangamagrama, Madhava of Sangamagrama - Contributions, Madhava of Sangamagrama - Kerala School of Astronomy and Mathematics
	www.experiencefestival.com /melpathur_narayana_bhattathiri (1755 words)

	Madhava
		Madhava is a name that can refer to: Vishnu The fourteenth century Indian mathematician, Madhava of Sangamagrama Other related archivesMadhava of Sangamagrama, Vishnu
		Madhava (Sanskrit) A name of Vishnu because of his slaying of the asura Madhu; applied to Krishna as an avataric manifestation of Vishnu; also the month corresponding to April-May.
		Some of his works were written in conjunction with his brother Madhava, who was the prime minister of Vira-bukka, also known as Madhavacharya, a celebrated teacher and scholar.
	www.experiencefestival.com /madhava (1072 words)

	Science Technology - General Information About Indian Economy, Government, Constitution, Education System
		The 14th century Indian mathematician Madhava of Sangamagrama, along with other mathematicians of the Kerala school, studied infinite series, convergence, differentiation, and iterative methods for solution of non-linear equations.
		Jyestadeva of the Kerala school wrote the first calculus text, the Yuktibhasa, which explores methods and ideas of calculus repeated only in 17th-century Europe.
		The other important names of historical astronomers from India are Madhava and Nilakantha Somayaji.
	www.bharatadesam.com /about/science_technology.php (3869 words)

	Canisius College - Dr. Sarada Rajeev
		This school, founded by Madhava of Sangamagrama and included as its prominent members Neelakanta Somayaji, Parameswara, Jyeshtadeva and Achyuta Panikkar, flourished between the 13th and 16th centuries-but has its intellectual roots with Aryabhatta who lived in the 5th century.
		We will review their knowledge of (pre-Keplerian, epicyclic) astronomy and the problems that they were attempting to solve that led them to such revolutionary mathematical discoveries.
		Hayashi, T. Kusuba and M. Yano, The correction of the Madhava series for the circumference of a circle, Centaurus 33 (2-3) (1990), 149-174.
	www.canisius.edu /topos/rajeev.asp (720 words)

	Madhava biography
		Madhava of Sangamagramma was born near Cochin on the coast in the Kerala state in southwestern India.
		Madhava discovered the series equivalent to the Maclaurin expansions of sin x, cos x, and arctan x around 1400, which is over two hundred years before they were rediscovered in Europe.
		Madhava also gave a table of almost accurate values of half-sine chords for twenty-four arcs drawn at equal intervals in a quarter of a given circle.
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Madhava.html (921 words)

	Reference.com/Encyclopedia/Madhava of Sangamagrama
		Perhaps Madhava's most significant contribution was in moving on from the finite procedures of ancient mathematics to 'treat their limit passage to infinity', which is considered to be the essence of modern classical analysis, and thus he is considered the founder of mathematical analysis.
		Madhava laid the foundations for the development of calculus, including differential calculus and integral calculus, which were further developed by his successors at the Kerala School.
		Some scholars have suggested that Madhava's work was transmitted to Europe via traders and Jesuit missionaries, and as a result, had an influence on later European developments in analysis and calculus.
	www.reference.com /browse/wiki/Madhava_of_Sangamagrama (1110 words)

	Madhava biography
		Madhava of Sangamagramma was born near Cochin on the coast in the Kerala state in southwestern India.
		Madhava discovered the series equivalent to the Maclaurin expansions of sin x, cos x, and arctan x around 1400, which is over two hundred years before they were rediscovered in Europe.
		Madhava also gave a table of almost accurate values of half-sine chords for twenty-four arcs drawn at equal intervals in a quarter of a given circle.
	www-history.mcs.st-and.ac.uk /Biographies/Madhava.html (921 words)

	Reference.com/Encyclopedia/Kerala school of astronomy and mathematics
		The Kerala School was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Kerala (South India), which included among its members: Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar.
		Little is known about Madhava, who lived near Kochi between the years 1340 and 1425.
		It is not known if Madhava discovered the other series as well, or whether they were discovered later by others in the Kerala school.
	www.reference.com /browse/wiki/Kerala_School (2673 words)

	info: Madhava_of_Sangamagrama (Site not responding. Last check: )
		The Kerala School was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Kerala, South India which included as its prominent members Parameshvara, Nilakantha Somayaji...
		ANAMIKACenturies ago, there used to be a great Mathematician called 'Madhava of Sangamagrama', one of the leading exponents of the (then) famous Kerala School of Mathematics.
		The 14th century Indian mathematician Madhava of Sangamagrama, along with other mathematicians of the Kerala school, studied infinite series, convergence, differentiation, and iterative methods for...
	www.napoli-pizza.net /Madhava_of_Sangamagrama.html (350 words)

	History of mathematics - Wikipedia, the free encyclopedia (Site not responding. Last check: )
		Madhava later in the 14th century computed the value of π to the eleventh decimal place as 3.14159265359.
		In the 7th century, Brahmagupta identified the Brahmagupta theorem, Brahmagupta's identity and Brahmagupta's formula, and for the first time, in Brahma-sphuta-siddhanta, he lucidly explained the use of zero as both a placeholder and decimal digit and explained the Hindu-Arabic numeral system.
		He also proved Rolle's theorem (a special case of the mean value theorem), studied Pell's equation, and investigated the derivative of the sine function.
	72.232.68.234 /cgi-bin/nph-proxy.cgi/010110A/687474703a2f2f656e2e77696b6970656469612e6f72672f77696b692f486973746f72795f6f665f6d617468656d6174696373 (4425 words)

	9 III. Madhava of Sangamagramma
		His most significant contribution was in moving on from the finite procedures of ancient mathematics to 'treat their limit passage to infinity', which is considered to be the essence of modern classical analysis.
		Both the approximations for sine and cosine functions to the second order of small quantities, (see over page) are special cases of Taylor series, (which are attributed to B Taylor).
		Several of the results are expressly attributed to him, for example Nilakantha quotes an alternate version of the sine series expansion as the work of Madhava.
	www-groups.dcs.st-and.ac.uk /~history/Projects/Pearce/Chapters/Ch9_3.html (831 words)

	Indian mathematics. Know more about Indian architecture, astronomy, mathematics, medicine, science.
		It was a school of mathematics and astronomy founded by Madhava of Sangamagrama, arguably the greatest mathematician-astronomer of medieval India.
		Although not completely certain, it is thought that Madhava was responsible for the discovery of many important mathematical results that were later re-discovered by eminent mathematicians (example: = tan - (tan3)/3 + (tan5)/5 -..., equivalent to Gregory series; also, p/4 = 1 - 1/3 + 1/5 - 1/7 +...
		Madhava's result, which gave a series for p, translated into the language of modern mathematics, reads: p R = 4R - 4R/3 + 4R/5 -...
	www.nriol.com /content/columns/ashok/indian-mathematics2.asp (1636 words)

	Carvaka Musings: Ancient Indian Mathematics
		Madhava also managed to calculate the value of pi to 17 decimal places (3.14155265358979324), much ahead of his contemporaries.
		Madhava of Sangamagrama was the founder of the Kerala School and considered to be one of the greatest mathematician-astronomers of the Middle Ages.
		It is vaguely possible that he may have written Karana Paddhati a work written sometime between 1375 and 1475 but all that is known of Madhava comes from works of later scholars.
	carvakamusings.blogspot.com /2006/08/ancient-indian-mathematics.html (2128 words)

	Mathematical analysis - ExampleProblems.com
		In the 12th century the Indian mathematician Bhaskara gave an example of what would now be called a "differential coefficient" and the basic idea behind what is now known as Rolle's theorem.
		The 14th century Indian mathematician Madhava of Sangamagrama expressed various trigonometric functions as infinite series, and estimated the magnitude of the error terms created by truncating these series.
		In Europe, analysis originated in the 17th century, with the independent invention of calculus by Newton and Leibniz.
	www.exampleproblems.com /wiki/index.php/Classical_analysis (707 words)

	Step Mathematics Worksheet Factory (Site not responding. Last check: )
		The University of Warwick also uses STEP papers in its admissions process, but their STEP exams are overseen by Cambridge.
		Madhava of Sangamagrama - Madhava (à¤®à¤¾à¤§à¤µ) of Sangamagrama (1350-1425) was a major mathematician from Kerala, in South India.
		He belonged to the Kerala school of mathematics and is considered the father of mathematical analysis for having taken the decisive step from the finite procedures of ancient mathematics to treat their limit-passage to infinity, which is the kernel of modern classical analysis.
	www.melbatone.com /Step/Mathematics-Worksheet-Factory.html (1737 words)

	circle, Moivre, Greek, value, showed, proved, known, irrational, first, correct, chronology, about, symbol - History of ... (Site not responding. Last check: )
		The Indian mathematician and astronomer Madhava* of Sangamagrama in the 14th century found the following infinite series expansion of π:
		Madhava also used the first 21 terms of the related series:
		In the 14th century, the Indian mathematician and astronomer Madhava* of Sangamagrama used
	www.alphasearch.org /History-of-.html (954 words)

	Newton, Isaac
		As with many areas of mathematics, calculus was developed through years of work by a number of different people.
		In particular, it was conceived and significantly developed by Indian mathematicians such as Bhaskara (1114–1185), Madhava of Sangamagrama (1340–1425), and members of the Kerala School founded by Madhava.
		In the Western world, the two who contributed the most to the development of calculus were Newton and Leibniz.
	www.newworldencyclopedia.org /preview/Isaac_Newton (5086 words)

	Melpathur Narayana Bhattathiri - Wikipedia, the free encyclopedia (Site not responding. Last check: )
		Melpathur Narayana Bhattathiri (1559-1632), third student of Achyuta Pisharati, was a member of Madhava of Sangamagrama's school of Astronomy and Mathematics.
		His masterpiece is considered the Prkriya-sarvawom, which sets forth an axiomatic system elaborating on the classical system of Panini.
		Learning Rg veda (adhyayanam) from Madhava, Tharka sastra (science of arguments in sanskrit) from Damodara, Vyakarana (sanskrit grammar) from Achyuta Pisharati, he became a pandit by the age of 16.
	www.selfobjects.com /mediawiki/index.php/Melpathur_Narayana_Bhattathiri (515 words)

	Sujit's world...
		The prominent figure during this time period is definitely Madhava of Sangamagramma.
		Though not fully certain, he is supposed to have independently derived taylor series expansion for arctan, sin, cos and many other function.
		A list of 13 different expansions attributed to Madhava is listed here.
	www.cds.caltech.edu /~nair/indianmathematics.php (2164 words)

	The Dispatch - Serving the Lexington, NC - News (Site not responding. Last check: )
		Archimedes was probably the first to discover the methods of Taylor series by using an infinite summation to achieve a finite trigonometric result.
		Liu Hui independently employed a similar method 400 years later, and about 800 years later, several examples of the use of Taylor series or closely-related methods were given by Madhava in the 14th century.
		Madhava of Sangamagrama (credited with the first use of "Taylor" series)
	www.the-dispatch.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Taylor_series (1201 words)

	Madhava at AllExperts
		Madhava is a name that can refer to:
		* Madhava of Sangamagrama, a fourteenth century Indian mathematician
		* Madhava (Madhvacharya), a renowned philosopher in the Vaishnavism tradition.
	en.allexperts.com /e/m/ma/madhava.htm (101 words)

	SCIENCE AND TECHNOLOGY IN ANCIENT INDIA : Encyclopedia Entry
		The 14th century Indian mathematician Madhava of Sangamagramma, along with other mathematicians of the Kerala school, studied infinite series, convergence, differentiation, and iterative methods for solution of non-linear equations.
		Jyestadeva of the Kerala school wrote the first calculus text, the Yuktibhasa, which explores methods and ideas of calculus repeated only in 17th-century Europe.
		The other important names of historical astronomers from India are Madhava and Nilakantha Somayaji.
	bibleocean.com /OmniDefinition/Science_and_technology_in_ancient_India (4359 words)

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