Ancient Babylonian Tablet Identified as the World's Oldest Trigonometry Table

Ancient Babylonian Tablet Identified as the World's Oldest Trigonometry Table

Plimpton 322 features four columns and 15 rows of numbers written in the cuneiform script of the time.

Traditionally, Greek astronomer Hipparchus is credited with inventing trigonometry around 120 B.C. However, this tablet predates the astronomer by over 1,000 years.

So how did the tablet help Babylonians do their sums?

Scientists recently decoded a clay tablet from ancient Babylonia that dates to around 3,700 years ago, and found that it contains the oldest trigonometric table in the world.

Those of you who can remember trigonometry can feel free to forget it, because ancient Babylonian mathematicians had a better way of doing it - using base 60!

"The 15 rows on the tablet describe a sequence of 15 right-angle triangles, which are steadily decreasing in inclination", they explained.

Plimpton 322, a 3,700-year-old Babylonian tablet held in the Rare Book and Manuscript Library at Columbia University in NY. He called it the world's oldest and the only completely accurate trigonometric table on record. "It is a fascinating mathematical work that demonstrates undoubted genius", said Dr. Daniel Mansfield, of the University of New South Wales' School of Mathematics and Statistics in Sydney, Australia, according to Newsweek.

"Bottom line is this: If interpreted as a trig table, it would be the oldest known".

Allen noted the most important finding from the tablet is the evidence of Pythagorean triples, indicating that Babylonians were seemingly aware of the Pythagorean theorem-years before Pythagoras.

The UNSW Sydney, whose scientists discovered the goal of the tablet, said the left-hand edge of the tablet is broken and the researchers build on previous research to present new mathematical evidence that there were originally six columns and that the tablet was meant to be completed with 38 rows.

"Our research reveals that Plimpton 322 describes the shapes of right-angle triangles using a novel kind of trigonometry based on ratios, not angles and circles".

One of the stronger theories was that it was a teaching aid for checking quadratic problems, but new research conducted by UNSW scientists Daniel Mansfield and Norman Wildberger now confirms the markings on the tablet as a trigonometry table.

Mansfield read about Plimpton 322 by chance and made a decision to study Babylonian mathematics after realising that it had parallels with the rational trigonometry of Wildberger's book Divine Proportions: Rational Trigonometry to Universal Geometry.

Plimpton 322's usefulness may not end with such applications, though. "With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own". The study authors expanded on prior research suggesting that Plimpton 322 was broken and incomplete, and they determined that there were originally six columns of figures on the tablet.

"It's rare that the ancient world teaches us something new".

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