Narayana pandit biography of william hill

Narayana (1340 - 1400) - Biography - MacTutor History of ...: Hayashi A. Plofker writes that his texts were the most significant Sanskrit mathematics treatises after those of Bhaskara II , other than the Kerala school. Mahalanobis Subrahmanyan Chandrasekhar C. Krishnaswamy Ayyangar — A.

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.

MacTutor History of Mathematics archive. You can help Wikipedia by expanding it. In other projects. The work anticipated many developments in combinatorics.



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 circle.

Indian mathematics. Siwan 18 4 , - Hayashi A. No comments:.

Narayana [4]:-

derived his rule for a segment of a circle from Mahavira's rule for an 'elongated circle' or an ellipse-like figure.
Narayana also gave a rule to calculate approximate values of a square root. He did this by using an indeterminate equation of the second order, Nx2+1=y2, where N is the number whose square root is to be calculated.

If x and y are a pair of roots of this equation with x<y then √N is approximately equal to xy​. To illustrate this method Narayana takes N= He then finds the solutions x=6,y=19 which give the approximation ​=, which is correct to 2 decimal places.

Narayana pandit biography of william hill Pearce Translated into the modern mathematical language of recurrence sequences :. Similarly to the work of Nilakantha it is almost unique in the history of Indian mathematics, in that it contains both proofs of theorems and derivations of rules. Narayana Pandit c.

Narayana then gives the solutions x=,y= which give the approximation ​=, correct to four places. Finally Narayana gives the pair of solutions x=,y= which give the approximation ​=, correct to eight decimal places. Note for comparison that √10 is, correct to 20 places, See [3] for more information.

The thirteenth chapter of Ganita Kaumudi was called Net of Numbers and was devoted to number sequences.

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    • For example, he discussed some problems concerning arithmetic progressions.

    The fourteenth chapter (which is the last one) of Naryana's Ganita Kaumudi contains a detailed discussion of magic squares and similar figures. Narayana gave the rules for the formation of doubly even, even and odd perfect magic squares along with magic triangles, rectangles and circles.

    He used formulae and rules for the relations between magic squares and arithmetic series.

    Biography of william shakespeare P Singh, Narayana's treatment of net of numbers, Ganita Bharati 3 1 - 2 , 16 - Narayana's cows sequence [ edit ]. Of great significance is the presence of mathematical proof inductive in Nilakantha 's work. Cross-references show.

    He gave methods for finding "the horizontal difference" and the first term of a magic square whose square's constant and the number of terms are given and he also gave rules for finding "the vertical difference" in the case where this information is given.

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      See THIS LINK.

    2. G G Joseph, The crest of the peacock(London, ).
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    4. T Hayashi, Narayana's rule for a segment of a circle, Ganita Bharati12()(),
    5. K Jha and J K John, The rules of arithmetic progression according to Narayana Pandita, Ganita-Bharati18()(),
    6. V Madhukar Mallayya, Various methods of squaring with special reference to the Lilavati of Bhaskara II and the commentary Kriyakramakari of Sankara and Narayana, Ganita Sandesh11(1)(),
    7. P Singh, Narayana's method for evaluating quadratic surds and the regular continued-fraction expansions of the surds, Math.

    10. Ed. (Siwan)18(2)(),

    11. P Singh, Narayana's rule for finding integral triangles, Math. Ed. (Siwan)18(4)(),
    12. P Singh, Narayana's treatment of magic squares, Indian J. Hist. Sci.21(2)(),
    13. P Singh, Narayana's treatment of net of numbers, Ganita Bharati3()(),
    14. P Singh, The Ganita Kaumudi of Narayana Pandita, Ganita-Bharati20()(),
    15. P Singh, Total number of perfect magic squares : Narayana's rule, Math.

      Ed. (Siwan)16(2)(),

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    Last Update November