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Acharya **Pingala**^{[2]} (Sanskrit: पिङ्गल, romanized: *Piṅgala*; c. 3rd–2nd century BCE)^{[1]} was an ancient Indian poet and mathematician,^{[3]} and the author of the * Chhandaḥśāstra* (Sanskrit: छन्दःशास्त्र, lit. 'A Treatise on Prosody'), also called the

Pingala | |
---|---|

Born | unclear, 3rd or 2nd century BCE^{[1]} |

Academic work | |

Era | Maurya or post-Maurya |

Main interests | Sanskrit prosody, Indian mathematics, Sanskrit grammar |

Notable works | Author of the "" (also called ChandaḥśāstraPingala-sutras), the earliest known treatise on Sanskrit prosody. Creator of Pingala's formula. |

Notable ideas | mātrāmeru, binary numeral system. |

The * Chandaḥśāstra* 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.

The * Chandaḥśāstra* presents a formula to generate systematic enumerations of metres, of all possible combinations of light (

- 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 syllable
- Append lists
*b*to list*a*and rename as list*x*

- Replicate list

Word length (n characters) |
Possible combinations |
---|---|

1 | G L |

2 | GG LG GL LL |

3 | 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.^{[11]} Pingala's binary representation increases towards the right, and not to the left as modern binary numbers usually do.^{[12]} 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 place values.^{[13]} Pingala's work also includes material related to the Fibonacci numbers, called * mātrāmeru*.

- A. Weber,
*Indische Studien*8, Leipzig, 1863. - Janakinath Kabyatittha & brothers,
*ChhandaSutra-Pingala*, Calcutta, 1931.^{[15]} - Nirnayasagar Press, Chand Shastra, Bombay, 1938
^{[16]}

- ^
^{a}^{b}Plofker, Kim (2009).*Mathematics in India*. Princeton University Press. pp. 55–56. ISBN 978-0-691-12067-6. **^**Singh, Parmanand (1985). "The So-called Fibonacci Numbers in Ancient and Medieval India" (PDF).*Historia Mathematica*.**12**(3). Academic Press: 232. doi:10.1016/0315-0860(85)90021-7. Archived from the original (PDF) on 2019-07-24. Retrieved 2018-11-29.**^**"Pingala – Timeline of Mathematics".*Mathigon*. Retrieved 2021-08-21.**^**Vaman Shivaram Apte (1970).*Sanskrit Prosody and Important Literary and Geographical Names in the Ancient History of India*. Motilal Banarsidass. pp. 648–649. ISBN 978-81-208-0045-8.**^**R. Hall,*Mathematics of Poetry*, has "c. 200 BC"**^**Mylius (1983:68) considers the Chandas-shāstra as "very late" within the Vedānga corpus.**^**François & Ponsonnet (2013: 184).**^**Van Nooten (1993)**^**Hall, Rachel Wells (February 2008). "Math for Poets and Drummers".*Math Horizons*.**15**(3). Taylor & Francis: 10–12. doi:10.1080/10724117.2008.11974752. JSTOR 25678735. S2CID 3637061. Retrieved 27 May 2022.**^**Shah, Jayant. "A History of Pingala's Combinatorics" (PDF).**^**Plofker (2009), 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."**^**Stakhov, Alexey; Olsen, Scott Anthony (2009).*The mathematics of harmony: from Euclid to contemporary mathematics and computer science*. World Scientific. ISBN 978-981-277-582-5.**^**B. van Nooten, "Binary Numbers in Indian Antiquity", Journal of Indian Studies, Volume 21, 1993, pp. 31–50**^**Susantha Goonatilake (1998).*Toward a Global Science*. Indiana University Press. p. 126. ISBN 978-0-253-33388-9.Virahanka Fibonacci.

**^***Chhanda Sutra – Pingala*.**^**Pingalacharya (1938).*Chand Shastra*.

- 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). - Van Nooten, B. (1993-03-01). "Binary numbers in Indian antiquity".
*Journal of Indian Philosophy*.**21**(1): 31–50. doi:10.1007/BF01092744. S2CID 171039636.

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