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Pingala (Devanagari: पिङ्गल ') is the traditional name of the author of the (also '), the earliest known Sanskrit treatise on prosody. Little is known about Piṅgala himself. In later Indian literary tradition, he is variously identified either as the younger brother of Pāṇini (4th century BC), or as Patañjali, the author of the Mahabhashya (2nd century BC).〔Maurice Winternitz, ''History of Indian Literature'', Vol. III〕 The ' is a work of eight chapters in the late Sūtra style, not fully comprehensible without a commentary. It has been dated to either the final centuries BC〔R. Hall, ''Mathematics of Poetry'', has "c. 200 BC"〕 or the early centuries AD,〔Mylius (1983:68) considers the Chandas-shāstra as "very late" within the Vedānga corpus.〕 at the transition between Vedic meter and the classical meter of the Sanskrit epics. This would place it close to the beginning of the Common Era, likely post-dating Mauryan times. 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.〔Van Nooten (1993)〕 The discussion of the combinatorics of meter corresponds to the binomial theorem. Halāyudha's commentary includes a presentation of the Pascal's triangle (called '). Pingala's work also contains the Fibonacci numbers, called '. Use of zero is sometimes mistakenly ascribed to Pingala due to his discussion of binary numbers, usually represented using 0 and 1 in modern discussion, while Pingala used light (''laghu'') and heavy (''guru'') 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). Positional use of zero dates from c. the 7th century (Brahmagupta) and would have been known to Halāyudha but not to Pingala. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Pingala」の詳細全文を読む スポンサード リンク
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