3,700 Year Old Trigonometry More Accurate Than Ours

Babylonian tablet trigonometry
Babylonian tablet “Plimpton 322” housed in the Rare Book and Manuscript Library, Columbia University. Credit: UNSW/Andrew Kelly.

It has long been said that Greek mathematician Hipparchus “fathered” trigonometry back in the second century BCE, but now Australian mathematicians have found evidence, inscribed in an ancient tablet, that Babylonians beat Hipparchus by at least 1,500 years.  And they say, the nearly 4,000 year old Babylonian trigonometry is more accurate than our own.



The tablet, known as “Plimpton 322” is 3,700 years old and is hardly new to the scientific community.  In fact, it was found by the infamous Edgar Banks, allegedly the man Indiana Jones is based on, in the early 1900s.  Cuneiform script, which scholars were able to decipher years ago, covers the tablet, so it has been common knowledge that Plimpton 322 is a number table.  What scholars couldn’t figure out is what the number table represented. 


For years, the scientific best guess has been that the Plimpton 322 tablet was a teacher’s aid, a cheatsheet of sorts used by instructors to check their students’ school work, But, exciting new research from mathematicians Daniel Mansfield and Norman Wildberger of the University of New South Wales, Sydney, suggests the tablet is actually an ancient Babylonian trigonometry table.  To make that leap, however, the duo had to let go of some modern trigonometry tenants.


First, the team had to reevaluate the number system with which they were working.  They discovered Babylonians used a 60 base number system that provides a higher degree of accuracy than our decimal system.


Second, they realized Babylonians used ratios instead of angles as the basis of their trigonometry.  According to the research team, the base number system coupled with ratios rather than angles makes Babylonian trigonometry more accurate than what we use today.


In a statement, Professor Wildberger said, 


“[Plimpton 322] opens up new possibilities not just for modern mathematics research, but also for mathematics education. With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own.”



The two published their work in Historia Mathematica.  Their article is open access and explains the math in great mathematical detail.  Anyone interested in such numerical ballet can click here (http://www.sciencedirect.com/science/article/pii/S0315086017300691) and enjoy.

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