Ancient Babylonian trigonometry table teaches us something new

Ancient “fascinating mathematical genius”

About 3 700 years ago a Babylonian mathematician wrote a trigonometry table on a clay tablet that scientists say is more accurate than anything we have today.

The table predates Pythagoras’s theorem by 1 000 years.

The four columns and 15 rows of cuneiform markings on the tablet represent the oldest and most accurate working trigonometric table in existence.

The tablet was probably used to survey land and to build temples, palaces and pyramids.

Excavated by archaeologist who was the inspiration for Indiana Jones

The diplomat, antiquities dealer and flamboyant amateur archaeologist Edgar Banks, who is said to have inspired the character of Indiana Jones, excavated the tablet in southern Iraq in the early 20th century.

Known as Plimpton 322, the tablet was named after the New York publisher George Plimpton, who bequeathed it to Columbia University in the 1930s as part of a major collection. Plimpton bought it from Banks.

Researchers find a novel kind of trigonometry

Daniel Mansfield of the University of New South Wales in Sydney says the tablet is “a fascinating mathematical work that demonstrates undoubted genius”.

The table makes use of a base 60, which is more accurate than the contemporary table which uses a base 10. It allows many more accurate fractions.

Mathematicians have tried to decipher the tablet for almost a century. Mansfield, who has published his research with his colleague Norman Wildberger in the journal Historia Mathematica says there had long been no agreement about the intended use of the tablet.

WATCH: Daniel Mansfield explains

“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.

“The tablet not only contains the world’s oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry.”

Great relevance for the modern world

Mansfield says it has great relevance for the modern world with possible practical applications in surveying, computer graphics and education.

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

Mansfield and Wildberger believe there is more to learn of Babylonian maths in untranslated or unstudied tablets.

“A treasure trove of Babylonian tablets exists, but only a fraction of them have been studied. This ancient but very sophisticated mathematical culture has much to teach us.”

 

 

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