Nārāyaṇa Paṇḍita ( sa, नारायण पण्डित) (1340–1400) was an Indian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. Plofker writes that his texts were the most significant Sanskrit mathematics treatises after those of Bhaskara II, other than the Kerala school. He wrote the '' Ganita Kaumudi'' (lit "Moonlight of mathematics") in 1356 about mathematical operations. The work anticipated many developments in

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many a ...

. About his life, the most that is known is that: Narayana Pandit wrote two works, an arithmetical treatise called ''Ganita Kaumudi'' and an

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...

ic treatise called ''Bijaganita Vatamsa''. Narayanan is also thought to be the author of an elaborate commentary of Bhaskara II's Lilavati, titled ''Karmapradipika'' (or ''Karma-Paddhati''). Although the ''Karmapradipika'' contains little original work, it contains seven different methods for squaring numbers, a contribution that is wholly original to the author, as well as contributions to algebra and

magic square In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number ...

s. Narayana's other major works contain a variety of mathematical developments, including a rule to calculate approximate values of square roots, investigations into the second order

indeterminate equation In mathematics, particularly in algebra, an indeterminate equation is an equation for which there is more than one solution. For example, the equation ax + by =c is a simple indeterminate equation, as is x^2=1. Indeterminate equations cannot be solv ...

''nq''² + 1 = ''p''² ( Pell's equation), solutions of indeterminate higher-order equations, mathematical operations with

zero 0 (zero) is a number representing an empty quantity. In place-value notation such as the Hindu–Arabic numeral system, 0 also serves as a placeholder numerical digit, which works by Multiplication, multiplying digits to the left of 0 by th ...

, several

geometrical Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

rules, methods of integer factorization, and a discussion of magic squares and similar figures. Evidence also exists that Narayana made minor contributions to the ideas of

differential calculus In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve ...

found in Bhaskara II's work. Narayana has also made contributions to the topic of

cyclic quadrilateral In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called the ''circumcircle'' or ''circumscribed circle'', and the vertices are said to be ''c ...

s. Narayana is also credited with developing a method for systematic generation of all permutations of a given sequence. Narayana's cows is an integer sequence which Narayana described as the number of cows present each year, starting from one cow in the first year, where every cow has one baby cow each year starting in its fourth year of life. The first few terms of the sequence are as follows: 1, 1, 1, 2, 3, 4, 6, 9, 13, 19, … Narayana's cows is sequence in

OEIS The On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences. It was created and maintained by Neil Sloane while researching at AT&T Labs. He transferred the intellectual property and hosting of the OEIS to the ...

. The ratio of consecutive terms approaches the supergolden ratio.

References

1340 births 1400 deaths Indian Hindus 14th-century Indian mathematicians {{asia-mathematician-stub