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Kriyakramakari (Kriyā-kramakarī) is an elaborate commentary in Sanskrit written by Sankara Variar and Narayana, two astronomer-mathematicians belonging to the Kerala school of astronomy and mathematics, on Bhaskara II's well-known textbook on mathematics Lilavati. Kriyakramakari ('Operational Techniques'), along with Yuktibhasa of Jyeshthadeva, is one of the main sources of information about the work and contributions of Sangamagrama Madhava, the founder of Kerala school of astronomy and mathematics. Also the quotations given in this treatise throw much light on the contributions of several mathematicians and astronomers who had flourished in an earlier era. There are several quotations ascribed to Govindasvami a 9th-century astronomer from Kerala. Sankara Variar (c. 1500 - 1560), the first author of Kriyakramakari, was a pupil of Nilakantha Somayaji and a temple-assistant by profession. He was a prominent member of the Kerala school of astronomy and mathematics. His works include ''Yukti-dipika'' an extensive commentary on Tantrasangraha by Nilakantha Somayaji. Narayana (c. 1540-1610), the second author, was a Namputiri Brahmin belonging to the Mahishamangalam family in Puruvanagrama (Peruvanam in modern-day Thrissur District in Kerala). Sankara Variar wrote his commentary of Lilavati up to stanza 199. Variar completed this by about 1540 when he stopped writing due to other preoccupations. Sometimes after his death, Narayana completed the commentary on the remaining stanzas in Lilavati. ==On the computation of π== As per K.V. Sarma's critical edition of Lilavati based on Kriyakramakari, stanza 199 of Lilavati reads as follows (Harvard-Kyoto convention is used for the transcription of the Indian characters): :vyAse bha-nanda-agni-hate vibhakte kha-bANa-sUryais paridhis sas sUkSmas/ :dvAviMzati-ghne vihRte atha zailais sthUlas atha-vA syAt vyavahAra-yogyas// This could be translated as follows; :"Multiply the diameter by 3927 and divide the product by 1250; this gives the more precise circumference. Or, multiply the diameter by 22 and divide the product by 7; this gives the approximate circumference which answers for common operations." Taking this verse as a starting point and commenting on it, Sanakara Variar in his Kriyakrakari explicated the full details of the contributions of Sangamagrama Madhava towards obtaining accurate values of π. Sankara Variar commented like this: :"The teacher Madhava also mentioned a value of the circumference closer (the true value ) than that: "Gods (), eyes (), elephants (), serpents (), fires (), three, qualities (), Vedas (), naksatras (), elephants (), arms () (2,827,433,388,233)—the wise said that this is the measure of the circumference when the diameter of a circle is nine nikharva ()." Sankara Variar says here that Madhava’s value 2,827,433,388,233 / 900,000,000,000 is more accurate than "that", that is, more accurate than the traditional value for π." Sankara Variar then cites a set of four verses by Madhava that prescribe a geometric method for computing the value of the circumference of a circle. This technique involves calculating the perimeters of successive regular circumscribed polygons, beginning with a square. 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「Kriyakramakari」の詳細全文を読む スポンサード リンク
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