[SunkenCiv]

Note: this topic is from 8/24/2017. Thanks BenLurkin . And kudos to PIF for pointing out that this isn't a Babylonian artifact, it's a Sumerian artifact.

[SunkenCiv]

• 3,700-year-old Babylonian tablet rewrites the history of maths - and shows the Greeks [tr] [2017]
• Mathematical mystery of ancient Babylonian clay tablet solved [2017]

What is the true role and meaning of Plimpton 322, the most famous mathematical clay tablet from Old Babylonian times? In this video Daniel and Norman explain their new theory: that Plimpton 322 was actually the world's first trigonometric table, but this was a ratio-based trigonometry, not an angle-based trigonometry. Remarkably, this table is also the world's only exact trigonometry table; all subsequent tables have been approximate.

To understand why, we need to understand how the OB scribes thought about triangles as half of a rectangle consisting of a short side, a long side and a diagonal. Ratios in such a triangle were based around their notion of ukullu, which they shared with the ancient Egyptians, who called it seqed. P322 turns out to allow someone to look up an exact integral triangle that approximates a single ratio of sides from a given triangle, and then to deduce other ratios: crucially without invoking a square root calculation.

The paper on which this video is based has been published in Historia Mathematica at http://www.sciencedirect.com/science/.... The title is "Plimpton 322 is Babylonian exact sexagesimal trigonometry" and it is by Daniel Mansfield and N J Wildberger from the School of Mathematics and Statistics, Faculty of Science, UNSW Sydney.

Old Babylonian mathematics and Plimpton 322: A new understanding of the OB tablet Plimpton 322 | Insights into Mathematics | Published on Aug 24, 2017