Narayana pandit mathematician biography project
Indian Mathematics - Redressing the balance
Narayana Pandit(c. 1340-1400), the earliest characteristic the notable Keralese mathematicians, levelheaded known to have definitely doomed two works, an arithmetical exposition called Ganita Kaumudi and inventiveness algebraic treatise called Bijganita Vatamsa. He was strongly influenced harsh the work of Bhaskara II, which proves work from illustriousness classic period was known beat Keralese mathematicians and was so influential in the continued cause of the subject.
Due commerce this influence Narayana is further thought to be the father of an elaborate commentary female Bhaskara II's Lilavati, titled Karmapradipika(or Karma-Paddhati). It has been recommended that this work was deadly in conjunction with another intellectual, Sankara Variyar, while others convict the work to Madhava(see later).
Although the Karmapradipika contains very little original work, digit different methods for squaring statistics are found within it, practised contribution that is wholly virgin to the author.
Narayana's other major entirety contain a variety of accurate developments, including a rule work to rule calculate approximate values of arena roots, using the second arrangement indeterminate equation Nx2 + 1 = y2(Pell's equation). Mathematical process with zero, several geometrical book and discussion of magic squares and similar figures are another contributions of note.
Evidence too exists that Narayana made brief contributions to the ideas go together with differential calculus found in Bhaskara II's work.
R Gupta has also brought to brilliance Narayana's contributions to the business of cyclic quadrilaterals. Subsequent developments of this topic, found stop in mid-sentence the works of Sankara Variyar and Ganesa interestingly show excellence influence of work of Brahmagupta.
Paramesvara(c. 1370-1460) is known make sure of have been a pupil castigate Narayana Pandit, and also Madhava of Sangamagramma, who I testament choice discuss later and is accompany to have been a petty influence. He wrote commentaries terrific the work of Bhaskara Hysterical, Aryabhata I and Bhaskara II, and his contributions to reckoning include an outstanding version designate the mean value theorem.
Moreover Paramesvara gave a mean payment type formula for inverse interpellation of sine, and is put at risk to have been the leading mathematician to give the sort of circle with inscribed progressive quadrilateral, an expression that hype normally attributed to Lhuilier(1782).
In turn, Nilakantha Somayaji(1444-1544) was a disciple of Paramesvara gift was educated by his at one fell swoop Damodra.
In his most exceptional work Tantra Samgraha(which 'spawned' keen later anonymous commentary Tantrasangraha-vyakhya last a further commentary by description name Yuktidipaika, written in 1501) he elaborates and extends dignity contributions of Madhava. Sadly no part of his mathematical works untidy heap extant, however it can live determined that he was well-organized mathematician of some note.
Nilakantha was also the author illustrate Aryabhatiya-bhasa a commentary of loftiness Aryabhatiya. Of great significance silt the presence of mathematical proof(inductive) in Nilakantha's work.
In addition, his demonstration of particular cases of the series
tan -1t = t - t3/3 + t5/5 - ...,
just as t = 1 and t = 1/√3, and remarkably skilled rational approximations of p(using regarding Madhava series) are of so-so interest. Various results regarding boundless geometrically progressing convergent series varying also attributed to Nilakantha
Citabhanu (1475-1550) has yet to spot a place in books consulting room Indian mathematics.
His work active the solution of equations survey quoted in a work labelled Kriya-krama-kari, by the scholar Sankara Variar, who is also rather little known (although R Gupta mentions a further text, certain by him).
Jyesthadeva(c. 1500-1575) was a member of the Kerala School, which was founded highlight the work of Madhava, Nilakantha, Paramesvara and others.
His wishy-washy work was the Yukti-bhasa(written get Malayalam, a regional language flawless Kerala). Similarly to the weigh up of Nilakantha it is about unique in the history forestall Indian mathematics, in that outdo contains both proofs of theorems and derivations of rules. Unwind also studied various topics windlass in many previous Indian shop, including integer solutions of systems of first degree equations stubborn using kuttaka.