Pingala


Pingala was an ancient Indian mathematician who authored the ', the earliest known treatise on Sanskrit prosody.
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. The 10th-century mathematician Halayudha wrote a commentary on the and expanded it.

Combinatorics

The ' 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. Halāyudha's commentary includes a presentation of Pascal's triangle. Pingala's work also includes material related to the Fibonacci numbers, called '.
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 and heavy rather than 0 and 1 to describe syllables. As Pingala's system ranks binary patterns starting at one, the nth pattern corresponds to the binary representation of n−1.
Pingala is credited with using binary numbers in the form of short and long syllables, a notation similar to Morse code. Pingala used the Sanskrit word śūnya explicitly to refer to zero.

Editions