The Fibonacci numbers or sequence is the numbers in the following integer Fibonacci numbers sequence: 0,1,1,2,3,5,8,13,21,34,55,89,14 … The Fibonacci sequence is named after Fibonacci, whose 1202 book ‘Liber Abaci’ brought the sequence to the mathematicians of the Europe. But the ancient Bharateeya mathematics already had it. The Fibonacci sequence appears with Sanskrit Prosody in the Bharateeya mathematics. According to Susantha Goonatilake, the development of the Fibonacci sequence is attributed in part to ‘Pingala’(200BC).As per Bharateeya ancient history ,this was associated with Virhanka (700AD), Gopala (1135AD),and Hemachandra (1150AD).
By definition , the first two numbers in the Fibonacci sequence are 1 and 1, or 0 and 1, depending on the chosen starting point of the sequence, and each subsequent number is the sum of the previous two. Parmanand Singh cites Pingala’s cryptic formula misrau cha ( the two are mixed ) and cites scholars who interpret it in that context. He dates Pingala before 450 BC.
However , in the work of Virhanka, the clearest exposition of the series arises. The own work of Virhanka is lost , but his work is available in a quotation by Gopala. The series is also discussed by Gopala and by the Jain scholar Hemachandra.One can see that the Sanskrit Prosody of thousands of year has travelled to other countries and they now call it as ‘Fibonacci Sequence’, but the truth of its origin in the ancient mathematical brilliance of Bharat is all too evident.
Nirmal Joshi Courtesy: Wah Bharat