Download Contributions to the History of Indian Mathematics by G.Emch, M.D.Srinivas, R.Sridharan (editors) PDF

By G.Emch, M.D.Srinivas, R.Sridharan (editors)

Articles at the heritage of Indian arithmetic, in accordance with the talks given on the periods on "History of Indian arithmetic" held throughout the first Joint-India-AMS assembly on arithmetic 2003

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Itimes. In particular,in the example of the g¯ ayatr¯ı metre, the numbers are 6, 15, 20, 15, 15, 6. L¯ıl¯ avat¯ı ([8], Appendix p. tbh, which is preceded by a general rule valid for any metre, given below. e 58 R. tt¯ an¯ am ˙ a tadvargo vargavarga´sca . up, has 8 syllables), the number of arrangements of the long and short syllables of all the p¯ adas is 232 = 4294967296. Evidently, the number of arrangements where the p¯ adas are all alike is the number of arrangements of the syllables in a single p¯ ada and is hence 28 = 256.

As along with the guru and laghu form the basis of all prosody. ) and many other commentators of Pingala’s ˙ work have the following couplet which expresses poetically the pre-eminence of the above ten units of prosody: myarastajabhnagairl¯ antaih. ebhirda´sabhiraks. araih. samastam v¯ a nmayam ˙ aptam a . vy¯ . u permeating the three worlds. a . as: adimadhy¯ ¯ avas¯ anes. u bhajas¯ a y¯ anti gauravam Pingala ˙ and Binary Arithmetic 43 yarat¯ a l¯ aghavam anti manau tu guru l¯ aghavam . y¯ Ñ Ý Ú× Ò£Õ × Ý ¦Ø ÇÖÚ º ÝÖØ Ð Ú Ý ¦Ø ÑÒÇ Ø ÞÐ Ú A rough translation in to English of the above ´sloka reads: The guru moves into the first, middle and the last position in bha, ja and sa.

Aram asandigdham aravat vi´svatomukham . s¯ astobham anavadyam ca s¯ u tram utravido viduh. . s¯ ËÔ Ö ¹ØÓ Ñ ×¦ ÒÚ × ÖÚØ ÚèØÓѠú ס» ס» Ú Ó Ú ¸ A s¯ utra should have the least number of syllables, should contain no doubtful words, no redundancy of words, should have unrestricted validity, should contain no meaningless words and should be faultless! The study of prosody which began in the vedic period evolved to apply to classical Sanskrit and to the Prakrit poetry as well and had its continued impact on the poetry of the later ages too.

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