Engravings on clay tablet confirm Babylonians knew Pythagoras Theorem before the man himself

‘Si.427’ is the name assigned to a clay tablet that has been estimated to be around 3,700 years old. While it purportedly depicts a land deal, the geometry in play is intriguing

August 07, 2021 by Sandipan Talukdar
Representational image. Photo : Wikimedia Commons

Engravings on an over 3000-year old clay tablet reinforce the belief that Pythagorean principles of geometry were known to the Babylonians centuries before Pythagoras himself, a recent study has said.

‘Si.427’ is the name assigned to a clay tablet (small cake-like structure) that has been estimated to be around 3,700 years old. This antique clay tablet belonged to the Old Babylonian Period between 1,900 and 1,600 BCE. However, this particular clay tablet is not a mere archaeological piece; the applied geometry engraved into it reveals many exciting facets of human knowledge about mathematics and its real-life applications.

The tablet was discovered during the late nineteenth century (1894) in what is now Iraq and was preserved in the Istanbul Archaeological Museum since then. Si.427 has the calculations of the Pythagorean triangle. This reinforces the fact that Pythagorean principles of geometry were known to the Babylonians over a millennium before Pythagoras, the Greek philosopher and mathematician, was even born.

The findings pertaining to Si.427 have been published in the journal Foundations of Science on August 4. The study was authored by Australian mathematician Dr. Daniel Mansfield of the University of New South Wales, Sydney, Australia.

Mansfield had also made an important finding previously about the Babylonian clay tablet containing geometrical calculations. Mansfield and Norman Wildberger, a researcher at the same university, had previously reported the oldest and most accurate trigonometric table. The tablet known as the Plimpton 322 described right-angled triangles using the Pythagorean principle – the sum of the squares of two numbers equals the square of the third number. The numbers are called the Pythagorean triples (For example – 32, 42 and 52).

Plimpton 322 was also from the Babylonian period and intrigued Mansfield enough that he began searching for other such clay tablets from the same period with the Pythagorean principle engraved; it eventually led him to the Si.427.

Commenting on the practical utility of such mathematical principles from ancient archaeological findings, Mansfield said: “You don’t just accidentally come up with trigonometry, you’re usually doing something practical.” Mansfield also revealed the purpose behind the tablet itself. The mathematical calculations on the tablet were written in the cuneiform script (an ancient script). Mansfield has been quoted saying the tablet actually depicts a field containing marshy areas along with a threshing floor and a nearby tower. “Si.427 is about a piece of land that’s being sold,” he commented.

The rectangles depicting the field have opposite sides of equal length, suggesting surveyors from back then had devised a way to create perpendicular lines more accurately than before, according to him.

“Much like we would today, you’ve got private individuals trying to figure out where their land boundaries are, and the surveyor comes out, but instead of using a piece of GPS equipment, they use Pythagorean triples. Once you understand what Pythagorean triples are, your society has reached a particular level of mathematical sophistication,” Mansfield reportedly said.

The Si.427 contained three Pythagorean triples — 3,4,5; 8,15,17 and 5,12,13.

Interestingly, the Si.427 was from a period when private land ownership had increased. What the clay tablets depict is the way the Babylonians were trying to solve land demarcation problems. They developed a mathematical way of doing it, and it is how particular mathematics developed to address some of the needs of the time.

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