The oldest and most precise trigonometric table in existence is a 3,700-year-old clay tablet from Babylon, implying that the Babylonians invented trigonometry more than 1,000 years before the Greeks.
The tablet, known as Plimpton 322, was found in what is now southern Iraq in the early 1900s, but scholars have never been able to determine what it was used for.
The enigma may have been resolved thanks to a team from the University of New South Wales (UNSW) in Australia. More than that, modern mathematicians could learn something from the Babylonian way of computing trigonometric values.
According to one of the researchers, Daniel Mansfield, “our analysis shows that Plimpton 322 specifies the geometry of right-angle triangles using a revolutionary sort of trigonometry based on ratios, not angles and circles.”
It is a wonderful mathematical achievement that exhibits unquestionable talent.
Early on, experts concluded that Plimpton 322 displayed a list of Pythagorean triples, which are collections of numbers that correspond to trigonometry models for calculating the angles of a right-angled triangle. What those triples were actually used for has been the topic of intense discussion.
Are they only a set of instructional activities, for instance? Or do they represent anything deeper?
Instead of the base 10 or decimal system that we use today, Babylonian mathematics employed a base 60 or sexagesimal system (similar to the minute marks on a clock face).
The researchers were able to demonstrate that the tablet would have initially had 6 columns and 38 rows by using Babylonian mathematical models. They also demonstrate how the numbers on the tablet might have been calculated using the Babylonian system by the mathematicians of the time.
The researchers hypothesize that calculations for the construction of palaces, temples, and waterways may have been made on the tablet by ancient scribes.
But if the results of the current study are accurate, Hipparchus, a Greek astronomer who flourished about 120 BC, was not the originator of trigonometry as has long been believed. The tablet is dated to between 1822 and 1762 BC.
It is also the earliest and most precise trigonometric table because of how the Babylonians handled mathematics and geometry.
The rationale is that a sexagesimal system requires less rounding up since it includes more precise fractions than a decimal system. A base 60 system has a much greater number of divisors than the two integers that may divide 10 exactly—2, and 5, respectively.
The researchers argue that we can use what we’ve learned today since cleaner fractions lead to less approximation and more precise computation.
This indicates that it is extremely pertinent to today’s society, according to Mansfield. Even though it has been out of use for more than 3,000 years, ancient mathematics might still be useful in fields like surveying, computer graphics, and education.
“This is a rare instance of the old world revealing fresh knowledge to us.”
Historia Mathematica has published the research. The UNSW team also created the following video to illustrate their findings.
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