Acharya Pingala

Acharya Pingala (pingala; around 3rd–2nd century BCE) was an ancient Indian poet and mathematician who wrote the Chandaḥśāstra (also known as the Pingala-sutras), the oldest known book on Sanskrit prosody.

The Chandaḥśāstra is an eight-chapter text written in the late Sūtra style that is incomprehensible without a commentary. It dates back to the last centuries BCE. In the 10th century, Halayudha elaborated on the Chandaḥśāstra in a commentary. According to legend, Pingala Maharshi was also the brother of Panini, the renowned Sanskrit grammarian and the first descriptive linguist.

Combinatorics

The Chandaḥśāstra provides the first description of a binary numeric system in relation to the methodical enumeration of metres with defined patterns of short and long syllables. The metre combinatorics discussion by Pingala corresponds to the binomial theorem. Halyudha’s 10th-century commentary on the Chandaḥśāstra has a statement of this theorem in what is now known as Pascal’s triangle (called meruprastra in the commentary), which was discovered by Halayudha and others centuries before Blaise Pascal. Pingala’s work also contains mātrāmeru., which relates to the Fibonacci numbers.

Pingala is attributed with the first use of binary numbers, describing the combinatorics of Sanskrit metre with light (laghu) and heavy (guru) syllables.

 As a result, Pingala is sometimes attributed with the first usage of zero, as he clearly referred to the number with the Sanskrit term nya. Pingala’s binary system of metre begins with four light laghu syllables as the first pattern (“0000” in binary), three light laghu and one heavy guru as the second pattern (“0001” in binary), and so on, such that the n-th syllable pattern corresponds to the binary to the binary representation of n − 1 {display style n-1} n-1 (with increasing positional values).

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