Pingala (
पिङ्गल ) was an
Ancient Indian writer, famous for his work,
the
Chandas Shastra ( , also
Chandas
Sutra ), a
Sanskrit treatise
on
prosody considered one of the
Vedanga. He developed advanced mathematical
concepts for describing the patterns of prosody.
In Indian
literary tradition, Pingala is identified as the younger brother of
Panini who according to tradition
were born in Shalatula. Panini was the great grammarian who
flourished in the 4th century BC. Other traditions identify him
with
Patanjali, the author of the
Mahabhashya.
Mylius (1983:68) considers the Chandas-shastra as "very late"
within the Vedanga corpus. This would place it close to the
beginning of the
Common Era, likely
post-dating
Mauryan times (R. Hall,
Mathematics of Poetry, has "c.
200
BC").
The shastra is divided into eight chapters. It was edited by Weber
(1863). It is at the transition between
Vedic meter and the classical meter of the
Sanskrit epics.The 10th century mathematician
Halayudha commented and expanded it. Pingala
presents the first known description of a
binary numeral system. He described
the binary numeral system in connection with the listing of Vedic
meters with short and long syllables. His discussion of the
combinatorics of meter, corresponds to the
binomial theorem. Halayudha' s commentary
includes a presentation of the
Pascal's triangle (called
meru-prastaara). Pingala's work also
contains the basic ideas of
Fibonacci
number (called
maatraameru ).
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.
Pingala is also another name of the deity Durga in Indian
mythology.
Editions
- A. Weber, Indische Studien 8, Leipzig,
1863.
- Bibliotheca Indica, Calcutta 1871-1874, reprint 1987.
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).
See also
External links