NationMaster - Encyclopedia: Virahanka

Virahanka (विरहाङ्क) was an Indian prosodicist who is also known for his work on mathematics. He possibly lived in the 6th century AD, but it is also possible that this date may be as late as 8th century. His work on prosody builds on the Chhanda-sutras of Pingala, and was the basis for a 12th c. commentary by Gopala. Prosody may mean several things: Prosody consists of distinctive variations of stress, tone, and timing in spoken language. ... Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ... (5th century — 6th century — 7th century — other centuries) Events The first academy of the east the Academy of Gundeshapur founded in Persia by the Persian Shah Khosrau I. Irish colonists and invaders, the Scots, began migrating to Caledonia (later known as Scotland) Glendalough monastery, Wicklow Ireland founded... (7th century — 8th century — 9th century — other centuries) Events The Iberian peninsula is taken by Arab and Berber Muslims, thus ending the Visigothic rule, and starting almost 8 centuries of Muslim presence there. ... Pingala (à¤ªà¤¿à¤™à¥à¤—à¤² ) is the supposed author of the Chandas shastra (, also Chandas sutra ), a Sanskrit treatise on prosody considered one of the Vedanga. ... Gopala was an Indian mathematician, who studied the Fibonacci numbers in 1135, more than half a century before Fibonacci popularized these numbers in Europe. ...

Contribution to Fibonacci Series

In an analysis of mAtrA-vrittas - 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 the 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 can be of length n, then we see that S(n+1) is obtained by adding a G at the end for all the S(n-1) strings and an L at 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 least four centuries of primacy over Fibonacci. In mathematics, the Fibonacci numbers form a sequence defined recursively by: In words: you start with 0 and 1, and then produce the next Fibonacci number by adding the two previous Fibonacci numbers. ... Leonardo of Pisa (1170s or 1180s â€“ 1250), also known as Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci, or, most commonly, simply Fibonacci, was an Italian mathematician, considered by some the most talented mathematician of the Middle Ages. ...

Subsequently commentaries by Gopala elaborated further on the sequence that 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.