|Born||unclear, 3rd / 2nd century BCE|
|Era||Maurya or post-Maurya|
|Main interests||Indian mathematics, Sanskrit grammar|
|Notable works||Author of the Chandastra (also called Pingala-sutras), the earliest known treatise on Sanskrit prosody|
|Notable ideas||m?tr?meru, binary numeral system, arithmetical triangle|
Pingala (Devanagari: pi?gala) (c. 3rd/2nd century BC) was an ancient Indian mathematician who authored the Chandastra (also called Pingala-sutras), the earliest known treatise on Sanskrit prosody.
The Chandastra is a work of eight chapters in the late S?tra style, not fully comprehensible without a commentary. It has been dated to the last few centuries BCE. The 10th century mathematician Halayudha wrote a commentary on the Chandastra and expanded it.
The Chandastra 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. Hal?yudha's commentary includes a presentation of Pascal's triangle (called meruprast?ra). Pingala's work also contains the Fibonacci numbers, called m?tr?meru.
Use of zero is sometimes ascribed to Pingala due to his discussion of binary numbers, usually represented using 0 and 1 in modern discussion, but Pingala used light (laghu) and heavy (guru) rather than 0 and 1 to describe syllables. As Pingala's system ranks binary patterns starting at one (four short syllables--binary "0000"--is the first pattern), the nth pattern corresponds to the binary representation of n-1 (with increasing positional values).
Pingala is credited with using binary numbers in the form of short and long syllables (the latter equal in length to two short syllables), a notation similar to Morse code. Pingala used the Sanskrit word nya explicitly to refer to zero.