The Hanging Gardens of Babylon. Image Credit: Martin Heemskerck
The Ancient Babylonians had known about Pythagoras' theorem over 1,000 years before he was even born.
The groundbreaking claim is based on a new analysis of a 3,700-year-old clay tablet known as 'Plimpton 322' which is inscribed with a demonstration of Babylonian mathematics.
According to researchers at the University of New South Wales, the tablet shows a form of trigonometry that wouldn't be developed by the Ancient Greeks for another ten centuries.
"Our research shows it's a trigonometric table so unfamiliar and advanced that in some respects it's superior to modern trigonometry," said mathematician Dr Daniel Mansfield.
"We've discovered these lines represent the ratios for a series of right-angled triangles ranging from almost a square to almost a flat line. This makes Plimpton 322 a powerful tool that could have been used for surveying fields or architectural calculations to build palaces, temples or step pyramids."
"The Babylonians unique approach to arithmetic and geometry means this is not only the world's oldest trigonometric table, it's also the only completely accurate trigonometric table on record."
Sexagesimal numbers survive in our reckoning of angles: minutes, degrees, and seconds.  A full circle, 360 degrees, 0 minutes, 0 seconds, divided by the rather simple sexagesimal term  114  35  30 comes very very close to the Pi  ratio. Substantially fewer digits, it appears, than required to express Pi to a similar degree of precision in the decimal system.
Pi is a ratio; one length compared to another. If you mean the circumference of a circle = 1, then the diameter is ~ 0.31831, which is 1 divided by Pi. Â
this makes perfect sense to me. this ratio based table would have been used to not only calculate the angle of the facing block when needed but also how tall and wide each step needs to be to keep a constant exact angle all the way up whther it be a smooth pyramid or facing OR steps.
There are three ghings I love about thos story: (1) the fact that Pythagoras' Theorem was known about more than 1000 years before Pyghagoras even lived; (2) that the Babylonians were making quite accurate and exact calculations using their sexagesimal number system long before anyone else; (3) their approach to trigonometry was entirely different from our modern one yet just as valid.
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