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| Timeline of mathematical innovation in South and West Asia ： ウィキペディア英語版 |
Timeline of mathematical innovation in South and West Asia
South and West Asia consists of a wide region extending from the present-day country of Turkey in the west to Bangladesh and India in the east.
==Timeline==
*3rd millennium BCE Sexagesimal system of the Sumerians:
*2nd millennium BCE Babylonian Pythagorean triples. According to mathematician S. G. Dani, the Babylonian cuneiform tablet Plimpton 322 written ca. 1850 BCE〔Mathematics Department, University of British Columbia, (''The Babylonian tablet Plimpton 322'' ).〕 "contains fifteen Pythagorean triples with quite large entries, including (13500, 12709, 18541) which is a primitive triple,〔Three positive integers form a ''primitive'' Pythagorean triple if and if the highest common factor of is 1. In the particular Plimpton322 example, this means that and that the three numbers do not have any common factors. However some scholars have disputed the Pythagorean interpretation of this tablet; see Plimpton 322 for details.〕 indicating, in particular, that there was sophisticated understanding on the topic" in Mesopotamia.
*1st millennium BCE Baudhayana Śulba Sūtras Earliest statement of Pythagorean Theorem: According to , the ''Śulba Sūtras'' contain "the earliest extant verbal expression of the Pythagorean Theorem in the world, although it had already been known to the Old Babylonians." The diagonal rope (') of an oblong (rectangle) produces both which the flank (''pārśvamāni'') and the horizontal (') produce separately." Since the statement is a ''sūtra'', it is necessarily compressed and what the ropes ''produce'' is not elaborated on, but the context clearly implies the square areas constructed on their lengths, and would have been explained so by the teacher to the student.〔
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