Babylonian Tablet Trigonometry
upstart writes:
Babylonian Tablet Trigonometry:
Contrary to what generations of pupils have learned in high school geometry, the Greek philosopher Pythagoras did not come up with this foundational theorem [(a^2 + b^2 = c^2)] first. The proof lies in an ancient artifact that dates back to the Old Babylonian (OB) period: 1900 to 1600 B.C.
In 1894, Father Jean-Vincent Scheil excavated a clay tablet at an archaeological expedition at Sippar, southwest of Baghdad. "But its significance was not understood at the time," Daniel Mansfield-lead author of the new research and a mathematician at the University of New South Wales in Sydney, Australia-writes in The Conversation.
The tablet, known as Si.427, is "the only known example of a cadastral document from the OB period, which is a plan used by surveyors to define land boundaries," according to Mansfield. On the front of the artifact is an inscription showing a diagram of a field. The surveyors drew a series of perpendicular lines, using Pythagorean triples to create precise right angles so that the fields' boundaries were as square as possible.
There's evidence of triangles drawn around the periphery of the field documented on the tablet, but if that's not enough proof, consider the back of the clay tablet. On it, cuneiform text describes the opposite side, including details about the sizes of the fields.
[...] Surveyors used Pythagorean triples to measure fields and draw accurate maps, but some numbers that make up Pythagorean triples aren't regular, and don't make sense to try to scale up to fit any field. Plimpton 322 lists a bunch of Pythagorean triples and notes which of their three values is regular, helping ancient Babylonian surveyors to quickly "do the math," so to speak.
Journal Reference:
Mansfield, Daniel F.. Plimpton 322: A Study of Rectangles [open], Foundations of Science (DOI: 10.1007/s10699-021-09806-0)
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