- Virahanka
Virahanka (विरहाङ्क) was an
India n prosodicist who is also known for his work onmathematics . He possibly lived in the6th century AD , but it is also possible that this date may be as late as8th century . His work on prosody builds on the "Chhanda-sutras" ofPingala , and was the basis for a 12th c. commentary byGopala .Contribution to Fibonacci Series
In an analysis of "mAtrA-vritta"s - combinations that obtain certain meters or "mAtrAs", Virhanka analyzes a mixture of short ("laghu") and long ("guru") syllables that appear in a meter.
For example, the "gAyAtri" mantra contains he string sa-vi-tur-va-reN-yam, in which tur and reN are long or guru, the others being short or laghu. Using G and L for guru and laghu, we can write this meter as LLGLGL, which is the kernel of the famous gAyAtri chhanda.
In the mAtrA-vritta analysis, G is taken to be twice as long as an L syllable, and Virahanka considers the question: in how many ways can we form meters of length n?
The answer emerges as follows:
Length 1: L (1)
Length 2: G, LL (2)
Length 3: LG, GL, LLL (3)
Length 4: GG, LLG, LGL, GLL, LLLL (5)
Length 5: LGG, GLG, LLLG, GGL, LLGL, LGLL, GLLL, LLLLL (8)If we denote S(n) as the number of ways in which a meter canbe of length n, then we see that S(n+1) is obtained by adding a G at the end for all theS(n-1) strings and an Lat the end for all the S(n) strings. Therefore S(n+1) = S(n)+S(n-1).
This is the well known
Fibonacci sequence . Thus, Virahanka has at leastfour centuries of primacy overFibonacci .Subsequently commentaries by Gopala elaborated further on the sequencethat now bears the name of Fibonacci. A 14th century text, "Prakrit-Paingala", also gives a formula for computing fibonacci numbers in terms of binomial coefficents.
ee also
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Indian mathematicians
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