Pingala (पिङ्गल piṅgalá) is the traditional name of the author of the Chandaḥśāstra (also Chandaḥsūtra), the earliest known Sanskrit treatise on prosody.

Nothing is known about Pingala himself. In Indian literary tradition, he is variously identified either as the younger brother of Panini (4th century BCE), or as Patanjali, the author of the Mahabhashya (2nd century BCE).^[1]

The chandaḥśāstra is a work of eight chapters in the late Sutra style, not fully comprehensible without a commentary. It has been dated to either the final centuries BCE^[2] or the early centuries CE,^[3] at the transition between Vedic meter and the classical meter of the Sanskrit epics. This would place it close to the beginning of the Common Era, likely post-dating Mauryan times. The 10th century mathematician Halayudha wrote a commentary on the chandaḥśāstra and expanded it.

[edit] Combinatorics

The chandaḥśāstra presents the first known description of a binary numeral system in connection with the systematic enumeration of meters with fixed patterns of short and long syllables. The discussion of the combinatorics of meter corresponds to the binomial theorem. Halayudha's commentary includes a presentation of the Pascal's triangle (called meruprastāra). Pingala's work also contains the basic ideas of Fibonacci number (called mātrāmeru ).

Use of zero is sometimes mistakenly ascribed to Pingala due to his discussion of binary numbers, usually represented using 0 and 1 in modern discussion, while Pingala used short and long syllables. Four short syllables (binary "0000") in Pingala's system, however, represented the number one, not zero. Positional use of zero dates from later centuries and would have been known to Halayudha but not to Pingala.

[edit] Editions

• A. Weber, Indische Studien 8, Leipzig, 1863.
• Bibliotheca Indica, Calcutta 1871-1874, reprint 1987.

[edit] Notes

[edit] References

• 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).

[edit] See also

• Chandas
• Sanskrit prosody
• Yamatarajabhanasalagah
• Indian mathematics
• Indian mathematicians

[edit] External links

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