He discovered the infinite series for arctan and sin and many methods for calculating the circumference of the circle. 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. All the terms are then divided by the odd num ...

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Madhava of Sangamagrama, Madhava of Sangamagrama - Contributions, Madhava of Sangamagrama - Kerala School of Astronomy and Mathematics

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Achyuta Pisharati - Works Achyuta Pisharati - Narayaneeyam

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Main article: Kerala school Madhava founded the Kerala school, which included as its prominent members Parameswara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. It flourished between the 13th and 16th centuries and has its intellectual roots with Aryabhatta who lived in the 5th century. The lineage continues down to modern times but the original research seems to have ended with Narayana Bhattathiri. These astronomers, in attempting to solve problems, invented revolut ...

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Madhava of Sangamagrama, Madhava of Sangamagrama - Contributions, Madhava of Sangamagrama - Kerala School of Astronomy and Mathematics

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Madhava is a name that can refer to: Vishnu The fourteenth century Indian mathematician, Madhava of Sangamagrama Other related archivesMadhava of Sangamagrama, Vishnu

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He discovered the technique of 'the reduction of the ecliptic'. He authored Sphuta-nirnaya (sphuta roughly meaning component parts<!not too sure!>, nirnaya meaning determining), Raasi-gola-sphuta-neeti (raasi meaning zodiac, gola meaning sphere and neeti roughly meaning rule), Karanottama (1593) and a 4 chapter treastise Uparagakriyakrama ...

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Achyuta Pisharati, Achyuta Pisharati - Works, Achyuta Pisharati - Narayaneeyam

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Pisharati is known to have scolded and provoked an errant Narayana to take up the Brahmin's duties of prayer and religious practices. He accepted Narayana as his Grammar student. Later when Pisharoti was struck with paralysis (or rheumatism by another account), Narayana, unable to bear the pain of his dear guru, by way of Gurudakshina took the disease upon himself. As a result Pisharoti is said to have been cured, but no medicine could cure Narayana. As a last resort, Narayana went to the Lord of Guruvayur and requested Thunjat Ramanujan Ezh ...

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Achyuta Pisharati, Achyuta Pisharati - Works, Achyuta Pisharati - Narayaneeyam

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Parameshvara (परमेश्वर) (1360-1425) was a major Indian mathematician of Madhava of Sangamagrama's Kerala school. He presented a series form of the sine function that is equivalent to its Taylor series expansion. Parameshvara - Birth. Paramesvara was born into a namboothiri brahmin family who were astrologers and astronomers. The family home was Vatasseri (also called Vatasreni) in the village of Alattur, Kerala. Paramesvara's coordinates with respect to Ujjain puts it at latitu ...

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Parameshvara - Birth Parameshvara - Work

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Madhava of Sangamagrama and the Kerala school were the first to come up with the important ideas of calculus in the 14th century and some [3] propose these ideas may have been transmitted to Europe by the 17th century. There is no evidence by way of relevant manuscripts but the evidence of methodological similarities, communication routes and a suitable chronology for transmission is hard to dismiss. In the controversy between Newton and Leibniz, suggestions were made that the work of Leibniz was not independent, as he claimed, but in ...

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History of calculus, History of calculus - Invention of Calculus, History of calculus - Controversy Newton Leibnitz... or Madhava?, History of calculus - Rigorous foundations, History of calculus - Integrals, History of calculus - Symbolic methods, History of calculus - Calculus of variations, History of calculus - Applications

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The Taylor series may also be generalised to functions of more than one variable with A second-order Taylor series expansion of a scalar-valued function of more than one variable can be compactly written as where is the gradient and is the Hessian matrix. Applying the multi-index notation the Taylor series for several variables becomes ...

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Taylor series, Taylor series - History, Taylor series - Properties, Taylor series - Taylor series for several variables, Taylor series - List of Taylor series of some common functions, Taylor series - Calculation of Taylor series

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Several important Taylor/Maclaurin series expansions follow. All these expansions are also valid for complex arguments x. Exponential function and natural logarithm: Geometric series: Binomial theorem: Trigonometric functions: Hyperbolic functions: See also:

Taylor series, Taylor series - History, Taylor series - Properties, Taylor series - Taylor series for several variables, Taylor series - List of Taylor series of some common functions, Taylor series - Calculation of Taylor series

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If this series converges for every x in the interval (a − r, a + r) and the sum is equal to f(x), then the function f(x) is called analytic. To check whether the series converges towards f(x), one normally uses estimates for the remainder term of Taylor's theorem. A function is analytic if and only if it can be represented as a power series; the coefficients in that power series are then necessarily the on ...

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Taylor series, Taylor series - History, Taylor series - Properties, Taylor series - Taylor series for several variables, Taylor series - List of Taylor series of some common functions, Taylor series - Calculation of Taylor series

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Greek mathematicians such as Eudoxus and Archimedes made informal use of the concepts of limits and convergence when they used the method of exhaustion to compute the area and volume of regions and solids. 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 th ...

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Mathematical analysis, Mathematical analysis - History, Mathematical analysis - Subdivisions

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Several methods exist for the calculation of Taylor series of a large number of functions. One can attempt to use the Taylor series as-is and generalize the form of the coefficients, or one can use manipulations such as substitution, multiplication or division, addition or subtraction of standard Taylor series to construct the Taylor series of a function, by virtue of Taylor series being power series. In some cases, one can also derive the Taylor series by repeatedly applying integration by parts. For example, consider the function for which we want a Taylor ...

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Taylor series, Taylor series - History, Taylor series - Properties, Taylor series - Taylor series for several variables, Taylor series - List of Taylor series of some common functions, Taylor series - Calculation of Taylor series

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(1st millennium – 2nd millennium – 3rd millennium – other millennia) 2nd millennium - Events. European crusades in Middle East Mongol Empires in Asia The Black Death The Renaissance in Europe The Protestant Reformation The agricultural and industrial revolutions The rise of nationalism and the nation state European discovery of the Americas and Australia and their colonization European colonization and decolonization in Afri ...

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2nd millennium - Events 2nd millennium - Significant persons 2nd millennium - Inventions, Discoveries, Introductions 2nd millennium - Centuries and Decades

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(1st millennium – 2nd millennium – 3rd millennium – other millennia) 2nd millennium - Events. European crusades in Middle East Mongol Empires in Asia The Black Death The Renaissance in Europe The Protestant Reformation The agricultural and industrial revolutions The rise of nationalism and the nation state European discovery of the Americas and Australia and their colonization European colonization and decolonization in Afri ...

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2nd millennium - Events 2nd millennium - Significant persons 2nd millennium - Inventions Discoveries Introductions 2nd millennium - Centuries and Decades

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Analysis is the generic name given to any branch of mathematics which depends upon the concepts of limits and convergence, and studies closely related topics such as continuity, integration, differentiability and transcendental functions. These topics are often studied in the context of real numbers, complex numbers, and their functions. However, they can also be defined and studied in any space of mathematical objects that is equipped with a definition of "nearness" (a topological space) or "distance" (a metric space). Mathematical analysis ...

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Mathematical analysis - History Mathematical analysis - Subdivisions

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Science and technology in ancient India covered all the major branches of human knowledge and activities, including mathematics, astronomy, physics, chemistry, medical science and surgery, fine arts, mechanical and production technology, civil engineering and architecture, shipbuilding and navigation, sports and games. Grant Duff, a British historian has remarked: “Many of the advances in the sciences that we consider today to have been made in Europe were in fact made in India centuries ago”. Science a ...

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Science and technology in ancient India - Introduction Science and technology in ancient India - Mathematics Science and technology in ancient India - Astronomy Science and technology in ancient India - Physics Science and technology in ancient India - Chemistry Science and technology in ancient India - Medicine & surgery Science and technology in ancient India - Fine arts Science and technology in ancient India - Production technology Science and technology in ancient India - Civil engineering & architecture Science and technology in ancient India - Shipbuilding & navigation Science and technology in ancient India - Games & Sports

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1425 - Events. Foundation of the Katholieke Universiteit Leuven, Belgium Masaccio writes The Holy Trinity (added by Mei) 1425 - Births. John II, Duke of Lorraine (died 1470) Edmund Sutton, English nobleman (died 1483) 1425 - Deaths. January 18 - Edmund Mortimer, 5th Earl of March, English politician (born 1391) March 17 - Ashikaga Yoshikazu, Japanese shogun (born 1407)

List of mathematicians - Aa — Ac. Abakanowicz, Bruno (Poland, 1852 – 1900) Abdelkader, Mostafa A. (?, ? – ) Abel, Niels Henrik (Norway, 1802 – 1829) Abelson, Harold (USA, ? – ) Al-Abhari Athir al-Din Mufaddal ibn Umar (Persia, 1200 – 1265) Abhyankar, Shreeram Shankar (India/USA, 1930 – ) Abouabdillah, Driss (Morocco, 1948 – ) Abraham, Ralph (USA, 1936 – ) Abramowitz, Milton (?, ? – ) Achenwall, Gottfried (Germany, 1719 – 1772) Ackerm ...

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List of mathematicians, List of mathematicians - A, List of mathematicians - Aa — Ac, List of mathematicians - Ad, List of mathematicians - Ag — Ak, List of mathematicians - Al, List of mathematicians - Am — An, List of mathematicians - Ap — Ar, List of mathematicians - As — Az, List of mathematicians - B, List of mathematicians - Ba, List of mathematicians - Be, List of mathematicians - Bh — Bi, List of mathematicians - Bl, List of mathematicians - Bo, List of mathematicians - Br, List of mathematicians - Bu, List of mathematicians - By — Bz, List of mathematicians - C, List of mathematicians - Ca, List of mathematicians - Ce — Ch, List of mathematicians - Cl — Co, List of mathematicians - Cr — Cs, List of mathematicians - Ct — Cz, List of mathematicians - D, List of mathematicians - Da, List of mathematicians - De, List of mathematicians - Di, List of mathematicians - Do — Dr, List of mathematicians - Du, List of mathematicians - Dw — Dz, List of mathematicians - E, List of mathematicians - Ea — Ef, List of mathematicians - Eg — El, List of mathematicians - Em — Er, List of mathematicians - Es — Ez, List of mathematicians - F, List of mathematicians - Fa, List of mathematicians - Fe, List of mathematicians - Fi, List of mathematicians - Fl — Fo, List of mathematicians - Fr, List of mathematicians - Fu — Fz, List of mathematicians - G, List of mathematicians - Ga, List of mathematicians - Ge, List of mathematicians - Gh — Gi, List of mathematicians - Gl — Go, List of mathematicians - Gr, List of mathematicians - Gu, List of mathematicians - Gy — Gz, List of mathematicians - H, List of mathematicians - Ha, List of mathematicians - He, List of mathematicians - Hi, List of mathematicians - Hl — Ho, List of mathematicians - Hr — Hu, List of mathematicians - Hy — Hz, List of mathematicians - I, List of mathematicians - J, List of mathematicians - Ja, List of mathematicians - Je — Jo, List of mathematicians - Ju — Jz, List of mathematicians - K, List of mathematicians - Ka, List of mathematicians - Ke, List of mathematicians - Kh — Ki, List of mathematicians - Kl — Ko, List of mathematicians - Kr, List of mathematicians - Ku — Kz, List of mathematicians - L, List of mathematicians - La, List of mathematicians - Le, List of mathematicians - Li, List of mathematicians - Ll — Lo, List of mathematicians - Lu, List of mathematicians - Ly — Lz, List of mathematicians - M, List of mathematicians - Ma, List of mathematicians - Mc — Me, List of mathematicians - Mi, List of mathematicians - Mo, List of mathematicians - Mu — Mz, List of mathematicians - N, List of mathematicians - Na — Ne, List of mathematicians - Ni — No, List of mathematicians - Nu — Nz, List of mathematicians - O, List of mathematicians - Oa — Om, List of mathematicians - On — Oz, List of mathematicians - P, List of mathematicians - Pa, List of mathematicians - Pe, List of mathematicians - Pf — Pi, List of mathematicians - Pl — Po, List of mathematicians - Pr, List of mathematicians - Pt — Pz, List of mathematicians - Q, List of mathematicians - R, List of mathematicians - Ra, List of mathematicians - Re, List of mathematicians - Rh — Ri, List of mathematicians - Ro, List of mathematicians - Ru — Rz, List of mathematicians - S, List of mathematicians - Sa, List of mathematicians - Sc, List of mathematicians - Se, List of mathematicians - Sh, List of mathematicians - Si, List of mathematicians - Sk — Sm, List of mathematicians - Sn — So, List of mathematicians - Sp, List of mathematicians - Sr — St, List of mathematicians - Su — Sy, List of mathematicians - Sz, List of mathematicians - T, List of mathematicians - Ta, List of mathematicians - Te — Th, List of mathematicians - Ti — To, List of mathematicians - Tr — Ts, List of mathematicians - Tu, List of mathematicians - Tv — Tz, List of mathematicians - U, List of mathematicians - V, List of mathematicians - Va, List of mathematicians - Ve — Vi, List of mathematicians - Vo — Vz, List of mathematicians - W, List of mathematicians - Wa, List of mathematicians - We, List of mathematicians - Wh, List of mathematicians - Wi, List of mathematicians - Wo — Wz, List of mathematicians - X, List of mathematicians - Y, List of mathematicians - Ya — Yo, List of mathematicians - Yu — Yz, List of mathematicians - Z, List of mathematicians - Za, List of mathematicians - Ze — Zh, List of mathematicians - Zi — Zz

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Melputhoor Narayana Bhattapathar is believed to have proceeded to the Guruvayoor Temple, located in Kerala state, India, on 19th Chingam of circa 761 ME - Malayalam Era, Malayalam calendar. There, he had written these verses and submitted before Guruvayoorappan, the presiding deity of Guruvayoor. These verses were submitted to the deity to get his chronic rheumatic disease cured as advised by his well wishers. He had completed the work in 100 days by submitting one cantos (of 10 verses, call ...

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Melpathur Narayana Bhattathiri, Melpathur Narayana Bhattathiri - Birth and Education, Melpathur Narayana Bhattathiri - The Narayaneeyam, Melpathur Narayana Bhattathiri - The legend

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