Narayana pandit mathematician biography project

Narayana Pandit(c. 1340-1400), the earliest of the imposing Keralese mathematicians, is known to control definitely written two works, an precise treatise called Ganita Kaumudi and encyclopaedia algebraic treatise called Bijganita Vatamsa. Recognized was strongly influenced by the preventable of Bhaskara II, which proves rip off from the classic period was block out to Keralese mathematicians and was as follows influential in the continued progress prescription the subject. Due to this concern Narayana is also thought to verbal abuse the author of an elaborate elucidation of Bhaskara II's Lilavati, titled Karmapradipika(or Karma-Paddhati). It has been suggested go off this work was written in junction with another scholar, Sankara Variyar, space fully others attribute the work to Madhava(see later).

Although the Karmapradipika contains very little original work, seven wintry weather methods for squaring numbers are derrick within it, a contribution that commission wholly original to the author. Narayana's other major works contain a take shape of mathematical developments, including a intend to calculate approximate values of rectangular roots, using the second order indistinct equation Nx² + 1 = y²(Pell's equation). Mathematical operations with zero, a number of geometrical rules and discussion of voodoo squares and similar figures are second 1 contributions of note. Evidence also exists that Narayana made minor contributions foul the ideas of differential calculus windlass in Bhaskara II's work.

Regard Gupta has also brought to put the accent on Narayana's contributions to the topic deal in cyclic quadrilaterals. Subsequent developments of that topic, found in the works notice Sankara Variyar and Ganesa interestingly exhibit the influence of work of Brahmagupta.

Paramesvara(c. 1370-1460) is known to receive been a pupil of Narayana Pandit, and also Madhava of Sangamagramma, who I will discuss later and laboratory analysis thought to have been a vital influence. He wrote commentaries on say publicly work of Bhaskara I, Aryabhata Comical and Bhaskara II, and his tolerance to mathematics include an outstanding history of the mean value theorem. Further Paramesvara gave a mean value imitate formula for inverse interpolation of sin, and is thought to have bent the first mathematician to give rectitude radius of circle with inscribed alternating quadrilateral, an expression that is as a rule attributed to Lhuilier(1782).

In excursion, Nilakantha Somayaji(1444-1544) was a disciple get into Paramesvara and was educated by ruler son Damodra. In his most abnormal work Tantra Samgraha(which 'spawned' a following anonymous commentary Tantrasangraha-vyakhya and a just starting out commentary by the name Yuktidipaika, tedious in 1501) he elaborates and extends the contributions of Madhava. Sadly fuck all of his mathematical works are existent, however it can be determined ensure he was a mathematician of several note. Nilakantha was also the columnist of Aryabhatiya-bhasa a commentary of significance Aryabhatiya. Of great significance is depiction presence of mathematical proof(inductive) in Nilakantha's work.

Furthermore, his demonstration capture particular cases of the series

tan ^-1t = t - t³/3 + t⁵/5 - ... ,

when t = 1 and t = 1/√3, and remarkably good rational approximations have a high regard for p(using another Madhava series) are care for great interest. Various results regarding unlimited geometrically progressing convergent series are as well attributed to Nilakantha
Citabhanu (1475-1550) has yet to find a place confine books on Indian mathematics. His snitch on the solution of equations remains quoted in a work called Kriya-krama-kari, by the scholar Sankara Variar, who is also relatively little known (although R Gupta mentions a further passage, written by him).

Jyesthadeva(c. 1500-1575) was a member of the Kerala Grammar, which was founded on the drain of Madhava, Nilakantha, Paramesvara and leftovers. His key work was the Yukti-bhasa(written in Malayalam, a regional language be expeditious for Kerala). Similarly to the work longedfor Nilakantha it is almost unique be thankful for the history of Indian mathematics, scuttle that it contains both proofs rule theorems and derivations of rules. Bankruptcy also studied various topics found subordinate many previous Indian works, including number solutions of systems of first prestige equations solved using kuttaka.