Pingala

 ( Fibonacci Numbers ) 

Acharya Pingala (; c. 3rd2nd century Common Era)

was an ancient Indian poet and mathematician, and the author of the (), also called the Pingala Sutras (), the earliest known treatise on Sanskrit prosody.

Vaman Shivaram Apte (1970). 9788120800458, Motilal Banarsidass. . ISBN 9788120800458

The is a work of eight chapters in the late Sūtra style, not fully comprehensible without a commentary. It has been dated to the last few centuries BCE.R. Hall, Mathematics of Poetry, has "c. 200 BC"Klaus Mylius (1983:68) considers the Chandas-shāstra as "very late" within the Vedānga corpus. In the 10th century CE, Halayudha wrote a commentary elaborating on the . According to some historians Maharishi Pingala was the brother of Pāṇini, the famous Sanskrit grammarian, considered the first descriptive linguist .. Others identify him as Patanjali, the 2nd century CE scholar who authored Mahabhashya.

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Combinatorics The presents a formula to generate systematic enumerations of metres, of all possible combinations of light ( laghu) and heavy ( guru) syllables, for a word of n syllables, using a recursive formula, that results in a partially ordered binary representation.Van Nooten (1993) Pingala is credited with being the first to express the combinatorics of Sanskrit prosody, e.g.:

• Create a syllable list x comprising one light ( L) and heavy ( G) syllable
• Repeat till list x contains only words of the desired length n
• Replicate list x as lists a and b
• Append syllable L to each element of list a
• Append syllable G to each element of list b
• Append lists b to list a and rename as list x

+ Possible combinations of Guru and Laghu syllables in a word of length n

G L

GG LG GL LL

GGG LGG GLG LLG GGL LGL GLL LLL

Because of this, Pingala is sometimes also credited with the first use of zero, as he used the Sanskrit word śūnya to explicitly refer to the number., pp. 54–56: "In the Chandah-sutra of Pingala, dating perhaps the third or second century BC, ... Pingala's use of a zero symbol śūnya as a marker seems to be the first known explicit reference to zero. ... In the Chandah-sutra of Pingala, dating perhaps the third or second century BC, there are five questions concerning the possible meters for any value "n". ... The answer is (2)⁷ = 128, as expected, but instead of seven doublings, the process (explained by the sutra) required only three doublings and two squarings – a handy time saver where "n" is large. Pingala's use of a zero symbol as a marker seems to be the first known explicit reference to zero." Pingala's binary representation increases towards the right, and not to the left as modern binary numbers usually do.

In Pingala's system, the numbers start from number one, and not zero. Four short syllables "0000" is the first pattern and corresponds to the value one. The numerical value is obtained by adding one to the sum of .B. van Nooten, "Binary Numbers in Indian Antiquity", Journal of Indian Studies, Volume 21, 1993, pp. 31–50 Pingala's work also includes material related to the Fibonacci numbers, called .

Susantha Goonatilake (1998). 9780253333889, Indiana University Press. . ISBN 9780253333889

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Editions

• Albrecht Weber, Indische Studien 8, Leipzig, 1863.
• Janakinath Kabyatittha & Brothers, Pingala Chhanda Sutram, Calcutta, 1931.
• Nirnayasagar Press, Chand Shastra, Bombay, 1938.

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Notes

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See also

• Chandas
• Sanskrit prosody
• Indian mathematics
• Indian mathematicians
• History of the binomial theorem
• List of Indian mathematicians

• Amulya Kumar Bag, 'Binomial theorem in ancient India', Indian J. Hist. Sci. 1 (1966), 68–74.
• George Gheverghese Joseph (2000). The Crest of the Peacock, p. 254, 355. Princeton University Press.
• Klaus Mylius, Geschichte der altindischen Literatur, Wiesbaden (1983).

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External links

• Math for Poets and Drummers, Rachel W. Hall, Saint Joseph's University, 2005.
• Mathematics of Poetry, Rachel W. Hall

Internet Archive, The Prosody of Pingala

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