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Ancient Tablet Reveals Babylonians Discovered Trigonometry (sciencemag.org)
An anonymous reader quotes a report from Science Magazine: Trigonometry, the study of the lengths and angles of triangles, sends most modern high schoolers scurrying to their cellphones to look up angles, sines, and cosines. Now, a fresh look at a 3700-year-old clay tablet suggests that Babylonian mathematicians not only developed the first trig table, beating the Greeks to the punch by more than 1000 years, but that they also figured out an entirely new way to look at the subject. However, other experts on the clay tablet, known as Plimpton 322 (P322), say the new work is speculative at best. Consisting of four columns and 15 rows of numbers inscribed in cuneiform, the famous P322 tablet was discovered in the early 1900s in what is now southern Iraq by archaeologist, antiquities dealer, and diplomat Edgar Banks, the inspiration for the fictional character Indiana Jones.
Now stored at Columbia University, the tablet first garnered attention in the 1940s, when historians recognized that its cuneiform inscriptions contain a series of numbers echoing the Pythagorean theorem, which explains the relationship of the lengths of the sides of a right triangle. (The theorem: The square of the hypotenuse equals the sum of the square of the other two sides.) But why ancient scribes generated and sorted these numbers in the first place has been debated for decades. Mathematician Daniel Mansfield of the University of New South Wales (UNSW) realized that the information he needed was in missing pieces of P322 that had been reconstructed by other researchers. He and UNSW mathematician Norman Wildberger concluded that the Babylonians expressed trigonometry in terms of exact ratios of the lengths of the sides of right triangles, rather than by angles, using their base 60 form of mathematics, they report today in Historia Mathematica.
Now stored at Columbia University, the tablet first garnered attention in the 1940s, when historians recognized that its cuneiform inscriptions contain a series of numbers echoing the Pythagorean theorem, which explains the relationship of the lengths of the sides of a right triangle. (The theorem: The square of the hypotenuse equals the sum of the square of the other two sides.) But why ancient scribes generated and sorted these numbers in the first place has been debated for decades. Mathematician Daniel Mansfield of the University of New South Wales (UNSW) realized that the information he needed was in missing pieces of P322 that had been reconstructed by other researchers. He and UNSW mathematician Norman Wildberger concluded that the Babylonians expressed trigonometry in terms of exact ratios of the lengths of the sides of right triangles, rather than by angles, using their base 60 form of mathematics, they report today in Historia Mathematica.
What kind of tablet was it? iPad or Android?
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Equating a table of pythagorean triples to Euclid is like equating the wheel that Oog invented in 50,000 BC to a Ferrari.
Babylonians don't get credit for trigonometry for being the first to use the concept of similar triangles.
Persians don't get credit for all of algebra because they were the first to write down the quadratic formula.
Aristotle doesn't get credit for absolutely all of math and logic because he invented modus ponens.
Eudoxus and/or Archimedes don't get credit (though arguably they should) for inventing calculus for discovering the method of exhaustion.
On the other hand, Euclid *does* get credit for inventing synthetic geometry and (basic) number theory, because Elements actually contains fleshed-out theories that still form a major part of what would be taught in a beginning course today.
There is a version of that story in the Sumerian literature too. Here is the Electronic Text Corpus of the Sumerian Language (ETCSL) link:
http://etcsl.orinst.ox.ac.uk/cgi-bin/etcsl.cgi?text=t.1.8.2.3#
See that "Preview" button?
That is what it does do. However, it requires that you have a ladder an integer number of units high, and place the bottom an integer number of units from the wall, and those integers must be in a predetermined ratio.
Basically, it is a list of triangles like 3,4,5 and 13,12,5 but, because they used base 60, there are a lot more of them in a given range.
However, the strategy for finding the answers in the table, and the way in which the table is laid out, are way more useful to builders and surveyors than the tables we used prior to calculators being invented, and the answers (for the values in the table) are more accurate than many tables generated before the use of computers, as the method relied entirely on manipulating integers, rather than 4 figure log tables generating decimals to a fixed number of figures by expounding a power series to a limited number of terms.
I was skeptical at first, but I am inclined to agree that it actually IS a different trigonometry, and it gives useful and practical results - but it does so by not solving the general case. However, it covers most cases that would be encountered by people using the technology of the day. (eg pyramid builders, land surveyors, and very probably boat builders). It is likely woefully inadequate for celestial navigation, but I have not tried it ;-)
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