Deciphered Ancient Tablet Reveals Babylonians' Mastery Over Mathematics

Deciphered Ancient Tablet Reveals Babylonians' Mastery Over Mathematics

Deciphered Ancient Tablet Reveals Babylonians' Mastery Over Mathematics

The tablet is arranged in a series of 15 rows intersected by four columns.

The Greek astronomer Hipparchus has widely been considered the father of trigonometry. Similarities in its writing style to that on other Babylonian tablets enabled experts to date it to between 1822 B.C. and 1726 B.C., around the time that King Hammurabi ruled the Babylonian Empire.

Researchers at the University of New South Wales in Sydney, Australia say they have discovered just that by studying the objective of a famous 3,700-year old Babylonian clay tablet called Plimpton 322, which they believe is actually the world's oldest and most accurate trigonometric table.

He wrote the paper with UNSW Associate Professor Norman Wildberger. The mathematicians demonstrate in their research how the Babylonians used a base of 60 in their numerical system instead of the more-modern base of 10 to generate numbers on the tablet. The tablet's rows describe a sequence of 15 right-angle triangles, decreasing in inclination.

The Plimpton 322 tablet is now housed in Columbia University's Rare Book and Manuscript Library in NY.

What's more, because of the way the Babylonians did their maths and geometry, it's the most accurate trigonometric table as well as the oldest.

Daniel Mansfield of the School of Mathematics and Statistics in the University of New South Wales (UNSW) Faculty of Science, Australia, says he has discovered the tablet's true meaning.

Plimpton 322-now the world's oldest known trigonometry table. Discovered in the early 1900s, the tablet has been of interest to mathematicians for years because it describes Pythagoras' theorem, yet is thought to have been created around 1800BC, more than a thousand years before Pythagoras was born and started tinkering with triangles.

'The huge mystery, until now, was its goal - why the ancient scribes carried out the complex task of generating and sorting the numbers on the tablet'.

"Apart from the column headings, the tablet just consists of columns of numbers, and this invites a great deal of purely mathematical speculation", said Melville in an emailed statement to National Geographic. Though the left edge of the tablet is broken, the researchers believe there were originally 6 columns and that the tablet was meant to be completed with 38 rows. "It is a fascinating mathematical work that demonstrates undoubted genius", Mansfield added.

Its use of ratio-based trigonometry rather than trigonometry based on angles and circles makes it the world's most accurate trigonometric table, Dr Mansfield says.

"With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own", Wildberger noted.

The tablet gets its name because it was in the collection of United States publisher George Plimpton and was donated to Columbia University in 1936 shortly before his death.

"This is a rare example of the ancient world teaching us something new".

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