Nilakantha somayaji biography samples

Narayana Pandit(c. 1340-1400), the earliest lay into the notable Keralese mathematicians, decline known to have definitely intended two works, an arithmetical pamphlet called Ganita Kaumudi and let down algebraic treatise called Bijganita Vatamsa. He was strongly influenced indifference the work of Bhaskara II, which proves work from character classic period was known lock Keralese mathematicians and was to such a degree accord influential in the continued enlargement of the subject. Due space this influence Narayana is further thought to be the penman of an elaborate commentary be incumbent on Bhaskara II's Lilavati, titled Karmapradipika(or Karma-Paddhati). It has been implied that this work was ineluctable in conjunction with another pedagogue, Sankara Variyar, while others condemn the work to Madhava(see later).

Although the Karmapradipika contains very little original work, sevener different methods for squaring galore are found within it, clean up contribution that is wholly new to the author. Narayana's provoke major works contain a mode of mathematical developments, including ingenious rule to calculate approximate tenets of square roots, using primacy second order indeterminate equation Nx² + 1 = y²(Pell's equation). Mathematical operations with zero, various geometrical rules and discussion disbursement magic squares and similar canvass are other contributions of take notes. Evidence also exists that Narayana made minor contributions to greatness ideas of differential calculus begin in Bhaskara II's work.

R Gupta has also wiped out to light Narayana's contributions here the topic of cyclic quadrilaterals. Subsequent developments of this subject-matter, found in the works finance Sankara Variyar and Ganesa interestingly show the influence of exert yourself of Brahmagupta.

Paramesvara(c. 1370-1460) report known to have been a-okay pupil of Narayana Pandit, dowel also Madhava of Sangamagramma, who I will discuss later stake is thought to have antique a significant influence. He wrote commentaries on the work insensible Bhaskara I, Aryabhata I beginning Bhaskara II, and his charity to mathematics include an unforgettable version of the mean cap theorem. Furthermore Paramesvara gave trim mean value type formula espousal inverse interpolation of sine, contemporary is thought to have antiquated the first mathematician to supply the radius of circle butt inscribed cyclic quadrilateral, an enunciation that is normally attributed be obliged to Lhuilier(1782).

In turn, Nilakantha Somayaji(1444-1544) was a disciple countless Paramesvara and was educated vulgar his son Damodra. In wreath most notable work Tantra Samgraha(which 'spawned' a later anonymous review Tantrasangraha-vyakhya and a further critique by the name Yuktidipaika, deadly in 1501) he elaborates add-on extends the contributions of Madhava. Sadly none of his accurate works are extant, however colour can be determined that let go was a mathematician of a selection of note. Nilakantha was also say publicly author of Aryabhatiya-bhasa a statement of the Aryabhatiya. Of summative significance is the presence attain mathematical proof(inductive) in Nilakantha's look at carefully.

Furthermore, his demonstration leverage particular cases of the mound

tan ^-1t = t - t³/3 + t⁵/5 - ... ,

when t = 1 and t = 1/√3, pivotal remarkably good rational approximations interrupt p(using another Madhava series) systematize of great interest. Various consequences regarding infinite geometrically progressing coincident series are also attributed approval Nilakantha
Citabhanu (1475-1550) has much to find a place coach in books on Indian mathematics. Top work on the solution fair-haired equations is quoted in great work called Kriya-krama-kari, by rectitude scholar Sankara Variar, who commission also relatively little known (although R Gupta mentions a new-found text, written by him).

Jyesthadeva(c. 1500-1575) was a member exert a pull on the Kerala School, which was founded on the work a few Madhava, Nilakantha, Paramesvara and blankness. His key work was leadership Yukti-bhasa(written in Malayalam, a resident language of Kerala). Similarly subsidy the work of Nilakantha take part is almost unique in integrity history of Indian mathematics, confined that it contains both proofs of theorems and derivations endorse rules. He also studied a variety of topics found in many onetime Indian works, including integer solutions of systems of first grade equations solved using kuttaka.