Acharya Pingala (; c. 3rd2nd century BCE) was an ancient Indian poet and mathematician, and the author of the (also called the Pingala-sutras), 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. In the 10th century CE, Halayudha wrote a commentary elaborating on the . According to some historians Maharshi Pingala was the brother of Pāṇini, the famous Sanskrit grammarian, considered the first descriptive linguist. Another think tank identifies him as Patanjali, the 2nd century CE scholar who authored Mahabhashya. Combinatorics The presents the first known description of a binary numeral system in connection with the systematic enumeration of metres with fixed patterns of short and long syllables. Pingala's work also includes material related to the Fibonacci numbers, called . Pingala is credited with the first use of binary numbers, using light (laghu) and heavy (guru) syllables to describe combinatorics of Sanskrit metre. Because of this, Pingala is sometimes also credited with the first use of zero, as he used the Sanskrit word śūnya to explicitly refer to the number. Pingala's binary system of metre starts 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, so that in general the -th syllable pattern corresponds to the binary representation of (with increasing positional values). Editions A. Weber, Indische Studien 8, Leipzig, 1863. Notes See also Chandas Sanskrit prosody Indian mathematics Indian mathematicians History of the binomial theorem List of Indian mathematicians 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). External links Math for Poets and Drummers, Rachel W. Hall, Saint Joseph's University, 2005. Mathematics of Poetry, Rachel W. Hall Fibonacci numbers Ancient Indian mathematicians Ancient Sanskrit grammarians Indian Sanskrit scholars 2nd-century BC mathematicians