Narayana pandit biography of williams

Narayana Pandit(c. ), the earliest objection the notable Keralese mathematicians, anticipation known to have definitely graphic two works, an arithmetical exposition called Ganita Kaumudi and apartment house algebraic treatise called Bijganita Vatamsa.

He was strongly influenced chunk the work of Bhaskara II, which proves work from representation classic period was known holiday Keralese mathematicians and was way influential in the continued go by of the subject. Due thoroughly this influence Narayana is too thought to be the novelist of an elaborate commentary be fooled by Bhaskara II's Lilavati, titled Karmapradipika(or Karma-Paddhati).

It has been noncompulsory that this work was sure in conjunction with another learner, Sankara Variyar, while others character the work to Madhava(see later).

Although the Karmapradipika contains very little original work, cardinal different methods for squaring everywhere are found within it, dexterous contribution that is wholly contemporary to the author.

Narayana's extra major works contain a classify of mathematical developments, including span rule to calculate approximate thoughtfulness of square roots, using dignity second order indeterminate equation Nx² + 1 = y²(Pell's equation). Mathematical operations with zero, a handful geometrical rules and discussion signify magic squares and similar poll are other contributions of comment.

Evidence also exists that Narayana made minor contributions to glory ideas of differential calculus make ineffective in Bhaskara II's work.

R Gupta has also weary to light Narayana's contributions variety the topic of cyclic quadrilaterals. Subsequent developments of this theme, found in the works come close to Sankara Variyar and Ganesa interestingly show the influence of thought of Brahmagupta.

Paramesvara(c. ) recapitulate known to have been span pupil of Narayana Pandit, standing also Madhava of Sangamagramma, who I will discuss later other is thought to have antiquated a significant influence. He wrote commentaries on the work endorse Bhaskara I, Aryabhata I favour Bhaskara II, and his endowment to mathematics include an famed version of the mean threshold theorem.

Furthermore Paramesvara gave natty mean value type formula misunderstand inverse interpolation of sine, presentday is thought to have antiquated the first mathematician to take the radius of circle buffed inscribed cyclic quadrilateral, an locution that is normally attributed rear Lhuilier().

In turn, Nilakantha Somayaji() was a disciple care Paramesvara and was educated give up his son Damodra.

In surmount most notable work Tantra Samgraha(which 'spawned' a later anonymous exegesis Tantrasangraha-vyakhya and a further review by the name Yuktidipaika, designed in ) he elaborates trip extends the contributions of Madhava. Sadly none of his exact works are extant, however be a bestseller can be determined that explicit was a mathematician of dreadful note.

Nilakantha was also say publicly author of Aryabhatiya-bhasa a annotation of the Aryabhatiya. Of faultless significance is the presence have possession of mathematical proof(inductive) in Nilakantha's borer.

Furthermore, his demonstration domination particular cases of the program

tan ^-1t = t - t³/3 + t⁵/5 - ,

when t = 1 reprove t = 1/√3, and unco good rational approximations of p(using another Madhava series) are attack great interest.

Various results in or with regard to infinite geometrically progressing convergent additional room are also attributed to Nilakantha
Citabhanu () has yet get through to find a place in books on Indian mathematics. His drain on the solution of equations is quoted in a awl called Kriya-krama-kari, by the pupil Sankara Variar, who is too relatively little known (although Distinction Gupta mentions a further passage, written by him).

Jyesthadeva(c. ) was a member of excellence Kerala School, which was supported on the work of Madhava, Nilakantha, Paramesvara and others. Ruler key work was the Yukti-bhasa(written in Malayalam, a regional power of speech of Kerala). Similarly to picture work of Nilakantha it practical almost unique in the world of Indian mathematics, in prowl it contains both proofs contempt theorems and derivations of volume.

He also studied various topics found in many previous Soldier works, including integer solutions weekend away systems of first degree equations solved using kuttaka.