Ancient tablet reveals genius who lived 3700 years ago

Ancient tablet reveals genius who lived 3700 years ago

Kenneth Drake
August 27, 2017

First we abandon the notion of angle, and instead describe a right triangle in terms of the short side, long side and diagonal of a rectangle. The study's authors note that this form of trigonometry is different from what's used today: it wouldn't use angles or approximations, because that base-60 system would allow mathematicians to use whole numbers, leading to exact calculations, which in turn would be useful for constructing fields, canals, or buildings.

Researchers have claimed that an ancient Babylonian tablet shows that the architects of Mesopotamia's ziggurats may well have understood trigonometry a millennium before its discovery by the Greeks. Intrigued, he teamed up with UNSW mathematician Norman Wildberger to study it. The infamous P322 tablet was discovered in the early 1900s in southern Iraq.

Its use of ratio-based trigonometry rather than trigonometry based on angles and circles makes it the world's most accurate trigonometric table, Dr Mansfield says.

These ancient mathematical inscriptions predate the earliest known evidence of trigonometry - thought to have originated around 120 B.C. with Greek astronomer Hipparchus - by approximately 1,000 years, the researchers reported in a new study.

No one is certain why the Babylonian trig system died out, even though we retained knowledge of zero and the base 60 system. The tablet which could have changed the method of calculation today is now available in the Rare Book and Manuscript Library at Columbia University in NY.

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The left edge of the tablet is broken, and the Australian researchers reckon that there were originally six columns. Babylonian mathematics may have been out of fashion for more than 3,000 years, but it has possible practical applications in surveying, computer graphics and education.

Mansfield said, "The huge mystery, until now, was [Plimpton 332's] purpose-why the ancient scribes carried out the complex task of generating and sorting the numbers on the tablet". A treasure-trove of Babylonian tablets exists, but only a fraction of them have been studied yet. "It is a fascinating mathematical work that demonstrates undoubted genius".

The Greek astronomer Hipparchus, who lived about 120 years BC, has always been regarded as the father of trigonometry, with his "table of chords" on a circle considered the oldest trigonometric table. The tablet was bequeathed to Columbia by publisher George Arthur Plimpton, who had purchased the artifact from Edgar Banks. "With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own", Wildberger noted.

The researchers believe that modern mathematics has a lot to learn from the simplicity and accuracy of Babylonian trigonometry. The tablet, known as Plimpton 322, was previously identified as a table filled with sets of Pythagorean triples, but nobody knew its goal was anything more than an educational tool. "The mathematical world is only waking up to the fact that this ancient but very sophisticated mathematical culture has much to teach us".