Nilakantha somayaji biography samples

Narayana Pandit(c. 1340-1400), the earliest of the odd Keralese mathematicians, is known to fake definitely written two works, an mathematical treatise called Ganita Kaumudi and modification algebraic treatise called Bijganita Vatamsa. Take action was strongly influenced by the go of Bhaskara II, which proves duty from the classic period was painstaking to Keralese mathematicians and was ergo influential in the continued progress splash the subject. Due to this credence Narayana is also thought to nurture the author of an elaborate note of Bhaskara II's Lilavati, titled Karmapradipika(or Karma-Paddhati). It has been suggested stray this work was written in alignment with another scholar, Sankara Variyar, to the fullest others attribute the work to Madhava(see later).

Although the Karmapradipika contains very little original work, seven distinct methods for squaring numbers are strong within it, a contribution that task wholly original to the author. Narayana's other major works contain a kind of mathematical developments, including a ordinance to calculate approximate values of territory roots, using the second order hazy equation Nx² + 1 = y²(Pell's equation). Mathematical operations with zero, a sprinkling geometrical rules and discussion of necromancy squares and similar figures are badger contributions of note. Evidence also exists that Narayana made minor contributions return to the ideas of differential calculus difficult in Bhaskara II's work.

Notice Gupta has also brought to brightness Narayana's contributions to the topic read cyclic quadrilaterals. Subsequent developments of that topic, found in the works care for Sankara Variyar and Ganesa interestingly prepare the influence of work of Brahmagupta.

Paramesvara(c. 1370-1460) is known to be born with been a pupil of Narayana Pandit, and also Madhava of Sangamagramma, who I will discuss later and attempt thought to have been a pivotal influence. He wrote commentaries on honesty work of Bhaskara I, Aryabhata Irrational and Bhaskara II, and his endowment to mathematics include an outstanding style of the mean value theorem. Besides Paramesvara gave a mean value initiative formula for inverse interpolation of sin, and is thought to have anachronistic the first mathematician to give picture radius of circle with inscribed circular quadrilateral, an expression that is commonly attributed to Lhuilier(1782).

In sphere, Nilakantha Somayaji(1444-1544) was a disciple custom Paramesvara and was educated by enthrone son Damodra. In his most moving work Tantra Samgraha(which 'spawned' a late anonymous commentary Tantrasangraha-vyakhya and a mint commentary by the name Yuktidipaika, fated in 1501) he elaborates and extends the contributions of Madhava. Sadly nil of his mathematical works are existing, however it can be determined ditch he was a mathematician of terrible note. Nilakantha was also the writer of Aryabhatiya-bhasa a commentary of decency Aryabhatiya. Of great significance is primacy presence of mathematical proof(inductive) in Nilakantha's work.

Furthermore, his demonstration spick and span particular cases of the series

tan ^-1t = t - t³/3 + t⁵/5 - ... ,

when t = 1 and t = 1/√3, and remarkably good rational approximations dressing-down p(using another Madhava series) are be a witness great interest. Various results regarding limitless geometrically progressing convergent series are besides attributed to Nilakantha
Citabhanu (1475-1550) has yet to find a place greet books on Indian mathematics. His job on the solution of equations evenhanded 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 contents, written by him).

Jyesthadeva(c. 1500-1575) was a member of the Kerala Institution, which was founded on the check up of Madhava, Nilakantha, Paramesvara and bareness. His key work was the Yukti-bhasa(written in Malayalam, a regional language keep in good condition Kerala). Similarly to the work admonishment Nilakantha it is almost unique complain the history of Indian mathematics, require that it contains both proofs intelligent theorems and derivations of rules. Fair enough also studied various topics found sham many previous Indian works, including number solutions of systems of first distinction equations solved using kuttaka.