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- Madhava_series abstract "In mathematics, a Madhava series is any one of the series in a collection of infinite series expressions all of which are believed to have been discovered by Madhava of Sangamagrama (c. 1350 – c. 1425), the founder of the Kerala school of astronomy and mathematics. These expressions are the infinite power series expansions of the trigonometric sine, cosine and arctangent functions, and the special case of the power series expansion of the arctangent function yielding a formula for computing π. The power series expansions of sine and cosine functions are respectively called Madhava's sine series and Madhava's cosine series. The power series expansion of the arctangent function is sometimes called Madhava–Gregory series or Gregory–Madhava series. These power series are also collectively called Taylor–Madhava series. The formula for π is referred to as Madhava–Newton series or Madhava–Leibnitz series or Leibniz formula for pi or Leibnitz–Gregory–Madhava series. These further names for the various series are reflective of the names of the Western discoverers or popularizers of the respective series.The derivations use many calculus related concepts such as summation, rate of change, and interpolation, which suggests that Indian mathematicians had a solid understanding of the basics of calculus long before it was developed in Europe. Other evidence from Indian mathematics up to this point such as interest in infinite series and the use of a base ten decimal system also suggest that it was possible for calculus to have developed in India almost 300 years before its recognized birth in Europe. No surviving works of Madhava contain explicit statements regarding the expressions which are now referred to as Madhava series. However, in the writing of later members of the Kerala school of astronomy and mathematics like Nilakantha Somayaji and Jyeshthadeva one can find unambiguous attributions of these series to Madhava. It is also in the works of these later astronomers and mathematicians one can trace the Indian proofs of these series expansions. These proofs provide enough indications about the approach Madhava had adopted to arrive at his series expansions.Unlike most previous cultures, which had been rather nervous about the concept of infinity, Madhava was more than happy to play around with infinity, particularly infinite series. He showed how, although one can be approximated by adding a half plus a quarter plus an eighth plus a sixteenth, etc, (as even the ancient Egyptians and Greeks had known), the exact total of one can only be achieved by adding up infinitely many fractions. But Madhava went further and linked the idea of an infinite series with geometry and trigonometry. He realized that, by successively adding and subtracting different odd number fractions to infinity, he could home in on an exact formula for π (this was two centuries before Leibniz was to come to the same conclusion in Europe). Through his application of this series, Madhava obtained a value for π correct to an astonishing 13 decimal places.".
- Madhava_series wikiPageExternalLink 9308.html.
- Madhava_series wikiPageID "26149716".
- Madhava_series wikiPageLength "29780".
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- Madhava_series wikiPageRevisionID "680508257".
- Madhava_series wikiPageWikiLink Arcminute.
- Madhava_series wikiPageWikiLink Arcsecond.
- Madhava_series wikiPageWikiLink Arctangent.
- Madhava_series wikiPageWikiLink Category:History_of_mathematics.
- Madhava_series wikiPageWikiLink Category:Kerala_school.
- Madhava_series wikiPageWikiLink Category:Mathematical_series.
- Madhava_series wikiPageWikiLink Cosine.
- Madhava_series wikiPageWikiLink Function_(mathematics).
- Madhava_series wikiPageWikiLink Gottfried_Leibniz.
- Madhava_series wikiPageWikiLink Gottfried_Wilhelm_Leibniz.
- Madhava_series wikiPageWikiLink Infinite_series.
- Madhava_series wikiPageWikiLink Inverse_trigonometric_functions.
- Madhava_series wikiPageWikiLink Isaac_Newton.
- Madhava_series wikiPageWikiLink Jya.
- Madhava_series wikiPageWikiLink Jyeshthadeva.
- Madhava_series wikiPageWikiLink Jyesthadeva.
- Madhava_series wikiPageWikiLink Jyeṣṭhadeva.
- Madhava_series wikiPageWikiLink Jyā,_koti-jyā_and_utkrama-jyā.
- Madhava_series wikiPageWikiLink K._V._Sarma.
- Madhava_series wikiPageWikiLink Katapayadi_system.
- Madhava_series wikiPageWikiLink Kerala_school_of_astronomy_and_mathematics.
- Madhava_series wikiPageWikiLink Kim_Plofker.
- Madhava_series wikiPageWikiLink Kojya.
- Madhava_series wikiPageWikiLink Kotijya.
- Madhava_series wikiPageWikiLink Laurent_series.
- Madhava_series wikiPageWikiLink Leibniz_formula_for_pi.
- Madhava_series wikiPageWikiLink Leibniz_formula_for_π.
- Madhava_series wikiPageWikiLink Madhava_of_Sangamagrama.
- Madhava_series wikiPageWikiLink Madhavas_sine_table.
- Madhava_series wikiPageWikiLink Mathematics.
- Madhava_series wikiPageWikiLink Minute_and_second_of_arc.
- Madhava_series wikiPageWikiLink Nilakantha_Somayaji.
- Madhava_series wikiPageWikiLink Padé_approximant.
- Madhava_series wikiPageWikiLink Puiseux_series.
- Madhava_series wikiPageWikiLink Sankara_Variar.
- Madhava_series wikiPageWikiLink Series_(mathematics).
- Madhava_series wikiPageWikiLink Sine.
- Madhava_series wikiPageWikiLink Tantrasamgraha.
- Madhava_series wikiPageWikiLink Taylor_Series.
- Madhava_series wikiPageWikiLink Taylor_series.
- Madhava_series wikiPageWikiLink Trigonometric_functions.
- Madhava_series wikiPageWikiLink Utkrama-jya.
- Madhava_series wikiPageWikiLink Western_world.
- Madhava_series wikiPageWikiLink Yuktibhasa.
- Madhava_series wikiPageWikiLink Yuktibhāṣā.
- Madhava_series wikiPageWikiLinkText "Madhava series".
- Madhava_series wikiPageWikiLinkText "Madhava series".
- Madhava_series wikiPageWikiLinkText "Madhava's arctangent series".
- Madhava_series wikiPageWikiLinkText "Madhava's cosine series".
- Madhava_series wikiPageWikiLinkText "Madhava's sine series".
- Madhava_series wikiPageWikiLinkText "power series expansions".
- Madhava_series wikiPageWikiLinkText "power series".
- Madhava_series hasPhotoCollection Madhava_series.
- Madhava_series wikiPageUsesTemplate Template:Cite_book.
- Madhava_series wikiPageUsesTemplate Template:Comparison_pi_infinite_series.svg.
- Madhava_series wikiPageUsesTemplate Template:Oclc.
- Madhava_series wikiPageUsesTemplate Template:Pi.
- Madhava_series wikiPageUsesTemplate Template:Refbegin.
- Madhava_series wikiPageUsesTemplate Template:Refend.
- Madhava_series wikiPageUsesTemplate Template:Reflist.
- Madhava_series wikiPageUsesTemplate Template:Sfrac.
- Madhava_series wikiPageUsesTemplate Template:Use_dmy_dates.
- Madhava_series subject Category:History_of_mathematics.
- Madhava_series subject Category:Kerala_school.
- Madhava_series subject Category:Mathematical_series.
- Madhava_series type School.
- Madhava_series type University.
- Madhava_series type Mathematician.
- Madhava_series type School.
- Madhava_series type University.
- Madhava_series comment "In mathematics, a Madhava series is any one of the series in a collection of infinite series expressions all of which are believed to have been discovered by Madhava of Sangamagrama (c. 1350 – c. 1425), the founder of the Kerala school of astronomy and mathematics.".
- Madhava_series label "Madhava series".
- Madhava_series sameAs m.0b6k5jd.
- Madhava_series sameAs Q6727285.
- Madhava_series sameAs Q6727285.
- Madhava_series wasDerivedFrom Madhava_series?oldid=680508257.
- Madhava_series isPrimaryTopicOf Madhava_series.