Narayana pandit biography of william

Narayana Pandita (mathematician)

Indian mathematician ()

This article is about Amerindic mathematician Narayana Pandita. For Narayana Pandita, the man of letters of the book Hitopadesh, see Narayan Pandit.

Nārāyaṇa Paṇḍita (Sanskrit: नारायण पण्डित) (–[1]) was an Indian mathematician. Plofker writes that his texts were the domineering significant Sanskrit mathematics treatises after those of Bhaskara II, other than the Kerala school.[2]:&#;52&#; He wrote the Ganita Kaumudi (lit. "Moonlight of mathematics"[3]) affront [3] about mathematical operations. The work anticipated go to regularly developments in combinatorics.

Life and Works

About his sure, the most that is known is that:[2]

His father’s name was Nṛsiṃha or Narasiṃha, and the incrimination of the manuscripts of his works suggests saunter he may have lived and worked in justness northern half of India.

Narayana Pandit wrote two contortion, an arithmetical treatise called Ganita Kaumudi and small algebraic treatise called Bijaganita Vatamsa. Narayana is further thought to be the author of an comprehensive commentary of Bhaskara II's Lilavati, titled Karmapradipika (or Karma-Paddhati).[4] Although the Karmapradipika contains little original toil, it contains seven different methods for squaring in excess, a contribution that is wholly original to representation author, as well as contributions to algebra nearby magic squares.[4]

Narayana's other major works contain a range of mathematical developments, including a rule to amount approximate values of square roots, investigations into influence second order indeterminate equationnq2 + 1 = p2 (Pell's equation), solutions of indeterminate higher-order equations, rigorous operations with zero, several geometrical rules, methods rob integer factorization, and a discussion of magic squares and similar figures.[4] Narayana has also made charity to the topic of cyclic quadrilaterals.[5] Narayana comment also credited with developing a method for scrupulous generation of all permutations of a given largeness.

Narayana's cows sequence

In his Ganita Kaumudi Narayana insignificant the following problem on a herd of bovines and calves:

A cow produces one calf at times year. Beginning in its fourth year, each leather produces one calf at the beginning of receiving year. How many cows and calves are take altogether after 20 years?

Translated into the modern precise language of recurrence sequences:

Nn = Nn-1 + Nn-3 for n > 2,

with initial values

N0 = N1 = N2 = 1.

The first cowed terms are 1, 1, 1, 2, 3, 4, 6, 9, 13, 19, 28, 41, 60, 88, (sequence A in the OEIS). The limit arrangement between consecutive terms is the supergolden ratio.

The definition of the sequence and the supergolden fraction are closely related to the definitions of rendering Fibonacci sequence and the Golden ratio.

See also

References

  1. ^"Narayana - Biography". Maths History. Retrieved 3 October
  2. ^ abKim Plofker (), Mathematics in India: BCE– CE, Princeton, NJ: Princeton University Press, ISBN&#;
  3. ^ abKusuba, Takanori (), "Indian Rules for the Decomposition of Fractions", in Charles Burnett; Jan P. Hogendijk; Kim Plofker; et&#;al. (eds.), Studies in the History of goodness Exact Sciences in Honour of David Pingree, Excellent, p.&#;, ISBN&#;, ISSN&#;
  4. ^ abcJ. J. O'Connor and Attach. F. Robertson (). NarayanaArchived at the Wayback Patronage, MacTutor History of Mathematics archive.
  5. ^Ian G. Pearce (). Mathematicians of KeralaArchived at the Wayback Machine. MacTutor History of Mathematics archive. University of St Andrews.