# Timeline of mathematical innovation in South and West Asia

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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 [1] "contains fifteen Pythagorean triples with quite large entries, including (13500, 12709, 18541) which is a primitive triple, [2] 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 ( Hayashi 2005 , p. 363), 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 (akṣṇayā-rajju) of an oblong (rectangle) produces both which the flank (pārśvamāni) and the horizontal (tiryaṇmānī) <ropes> produce separately." [3]

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. [3]

## Notes

1. Mathematics Department, University of British Columbia, The Babylonian tablet Plimpton 322.
2. Three positive integers ${\displaystyle (a,b,c)}$ form a primitive Pythagorean triple if ${\displaystyle c^{2}=a^{2}+b^{2}}$ and if the highest common factor of ${\displaystyle a,b,c}$ is 1. In the particular Plimpton322 example, this means that ${\displaystyle 13500^{2}+12709^{2}=18541^{2}}$ 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.
3. ( Hayashi 2005 , p. 363)

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