The clay tablet, also known as Plimpton 322 or P322, is an exact ratio-based trigonometric table.
We can all relate Pythagoras to his well-known theorem, which establishes that the square of the longest side of a triangle — hypotenuse — equals the sum of both remaining squares. For centuries, this was one of the most accurate mathematician conceptions, which positioned the Greeks as one of the most advanced cultures in the world. However, a recent discovery suggests Babylonians actually had prior and more exact knowledge of trigonometry.
According to the recent report in Science Mag, “This ancient Babylonian tablet may contain the first evidence of trigonometry,” Plimpton 322 was first discovered by in the early 1900’s in Iraq by Edgar Banks, an archaeologist, diplomat and antiquities dealer. Subsequently, the tablet caught the eye of investigators in 1940, when “historians recognized that its cuneiform inscriptions contained a series of numbers echoing the Pythagorean theorem.”
In the years that followed, experts tried unsuccessfully to decode the ancient tablet secrets. Until Dr. Daniel Mansfield, part of the Faculty of Science at the School of Mathematics and Statistics in the University of New South Wales, came across it. Dr. Mansfield and his research team discovered that P322 traces the forms of right-angle triangles using ratios, instead of angles and circles.
According to the original report “Plimpton 322 is Babylonian exact sexagesimal trigonometry” published August 24th in Historia Mathematica — the official journal of the International Commission on the History of Mathematics — Dr. Mansfield refers to the relevance of the tablet. “It is a fascinating mathematical work that demonstrates undoubted genius. The tablet not only contains the world’s oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry.”
Although the existence of this tablet suggests Babylonians discovered the exact sexagesimal trigonometry 1,500 years before the Greeks, Dr. Mansfield considers further research should be done. “On the mathematical side it is becoming increasingly clear that the OB tradition of step-by-step procedures based on their concrete and powerful arithmetical system is much richer than we formerly imagined. Perhaps the understanding of this ancient culture can help inspire new directions in modern mathematics and education.”
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