Narayana pandit mathematician biography project

This piece is the last in a series of essays on Indian astronomy and mathematics. Read the previous piece by the author here.

The Classical Era Continues

For centuries after Bhaskara, the classical era continued. The Ganita Kaumudi of Narayana Pandita is a fascinating book, with an interesting structure and several novelties. Like Mahavira, he gave both rules and a series of examples. He expanded Aryabhata’s formula for sum of series of numbers, their squares, and cubes, to any arbitrary power.

Effectively, he provided the formula

(Sn)r = [n(n+1)(n+2)…(n+r)] / [….(r+1)]

Narayana also expanded on the meru prastaras (Pascal’s triangles) of Pingala and Hemachandra into more elaborate versions. Permutations, combinations, areas and volumes of more complex geometric shapes were other areas of exploration and explanation.

His famous novelty was magic squares, squares filled with numbers so that each row and column add up to the same number. He explained procedures to create magic squares of desired sizes, how to fill them up for a given total, and certain fascinating variations, including use of negative numbers.

He extended this to magic rectangles, and other figures, like squares within

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India's narayan-pandit[1]

1. 05/08/15 1India's Effort to Geometry India's Endeavor to Geometry Narayan Pandit Presented by:- Mrs . Geeta Ghormade Innovation & Research Room , MGS Nagpur

2. 05/08/15 2India's Contribution accomplish Geometry Scripts: 1) Comb arithmetical treatise - Ganit Kaumudi, 2) An algebraical treatise – Bijaganita Vatamsa •Lived mission 14th hundred AD delete the space of ( - ) •Mathematician draw round medieval interval . •Kerala School be the owner of Mathematics Narayan Pandit

3. Ganit Kaumudi 05/08/15 India's Contribution permission Geometry 3 Chapter 4 - Triangles, quadrilaterals, prepare, their areas, formation strip off integral trigon and quadrilaterals, cyclic quadrilaterals

4. 05/08/15 4India's Endeavor to Geometry Formulae answer Triangle • Area returns triangle = • Theorize a, b, c tricky sides sustaining the trilateral and s is semifinal perimeter i.e. 2 s = a + b + c then Component of trilateral = [s (s-a) (s-b) (s- c)]1/2 • Circum radius = • r of incised circle = 2 HeightBase × peak sidesofproduct ×2 Perimetrer Area×2

5. 05/08/15 5India's Gift to Geometry Narayana’s Results for Circum radius 1) R = [ BC2 + {(AD2 - BD × DC)/AD}2 ]1/2 2) R = A B C D 2 1 2 1 altitudesofproduct flanksofproductdiagonalsofoduct ×Pr

6. 05/08/15 India's Contributi

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Narayana Pandit

Biography

Narayana was the son of Nrsimha (sometimes written Narasimha). We know that he wrote his most famous work Ganita Kaumudi on arithmetic in but little else is known of him. His mathematical writings show that he was strongly influenced by Bhaskara II and he wrote a commentary on the Lilavati of Bhaskara II called Karmapradipika. Some historians dispute that Narayana is the author of this commentary which they attribute to Madhava.

In the Ganita Kaumudi Narayana considers the mathematical operation on numbers. Like many other Indian writers of arithmetics before him he considered an algorithm for multiplying numbers and he then looked at the special case of squaring numbers. One of the unusual features of Narayana's work Karmapradipika is that he gave seven methods of squaring numbers which are not found in the work of other Indian mathematicians.

He discussed another standard topic for Indian mathematicians namely that of finding triangles whose sides had integral values. In particular he gave a rule of finding integral triangles whose sides differ by one unit of length and which contain a pair of right-angled triangles having integral sides with a common integral height. In terms of geometry Narayana gave a rule for a segment of a c