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Chandaḥśāstra — Pingala

~300 BC · Transmission: Silenced
MathematicsMethodIndian

Pingala writes the Chandaḥśāstra ('Science of Meters') as a treatise on Sanskrit prosody, classifying all possible meters through combinations of long (guru, G) and short (laghu, L) syllables. In systematically enumerating these combinations he introduces a binary representation system: the prastāra algorithm recursively generates all combinations of n syllables, equivalent to modern binary enumeration. Halayudha's commentary (10th century) makes explicit Pascal's triangle (meru-prastāra), implicitly contained in the text. The Chandaḥśāstra also contains the first explicit reference to zero as a marker (śūnya). Leibniz independently develops the binary system c. 1679 without knowing of Pingala; the independence is complete and both traditions are valid.

InstitutionVedanga tradition of Sanskrit prosody
Historical regionNorthern India (exact location unknown)
Primary sourceChandaḥśāstra, Pingala, c. 3rd-2nd century BC — edition with Halayudha's commentary: Kedāranātha, Calcutta, 1871; modern analysis: Plofker, K., Mathematics in India, Princeton UP, 2009, pp. 54-56
Secondary sourceWikipedia (verified): en.wikipedia.org/wiki/Pingala; ResearchGate — Sanskrit Prosody, Piṅgala Sūtras and Binary Arithmetic
Original languageLate Vedic Sanskrit (highly compressed sutra, requires commentary to interpret)
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