# This 3,700-year-old clay tablet shows applied engineering

A mathematician from Australia knows for sure: this 3,700-year-old tablet is the oldest example of applied engineering. Not everyone agrees.

You may have heard of the Pythagorean Theorem, which refers to the relationship between the lengths of the sides of a right triangle (ie, at an angle of 90 degrees). And when I heard the name Pythagoras, I immediately thought without doubt of the form “his”: a2+ b2= c2.

Archaeologists have long known that the Greek mathematician was not the originator of this theory; For example, in ancient Babylon the formula was already used. In fact, the Babylonians applied this formula a thousand years before Pythagoras. This is the conclusion of Australian researcher Daniel Mansfield of the University of New South Wales, after studying a very ancient clay slab.

### C 427

The tablet, called Si.427, dates from the Old Babylonian period between 1900 and 1600 BC and was published in the late 19th century.From A century discovered in what is now Iraq. The artifact remained in the Istanbul Archaeological Museum for years before it was placed by Mansfield and his colleague Norman Wildberger.

The two had been searching for clay tablets from ancient Babylonia for some time, including Plimpton 322. At the time, scholars have speculated that the tablet may have had some practical uses, perhaps in surveying or construction. Plimpton 322 led Mansfield and Wildberger to examine more artifacts from the same period, and the masters arrived at Si 427.

### Pythagorean triplets

After examining the ancient clay piece in detail, the researchers concluded that Si 427 shows a plot of land that has been sold. The tablet describes a field with swampy areas, as well as the floor of a threshing floor and a nearby tower. The rectangles depicting the field have opposite sides of equal length.

Manfield was particularly interested in the accuracy with which the boundaries of the field are determined. According to the mathematician, the ancient Babylonians achieved this accuracy using the so-called Pythagorean triples. These are three positive numbers (i.e. above 0) which a2+ b2= c2
applies. The image below shows an example of a Pythagorean triple.

This makes the 3,700-year-old tablet, according to Mansfield, the oldest evidence of trigonometry, called trigonometry. Plimpton 322 is also about 3,700 years old, and also shows trigonometry, but the Australian estimates Si.427 to be much older.

### First clue?

But the Assyriologist Matthew Osendriever, who studies Babylonian astrology and mathematics at the Free University of Berlin, disputes this claim. The author explained that in Si.427, Pythagorean numbers are used to generate rectangles with perpendicular sides. And as far as we know, this is already the first example of such a field account in which this is done.”

“It is certainly not the first evidence of applied geometry, because (approximate) superficial accounts of various geometric figures have been found long before this tablet, giving rise to the Pythagorean numbers without creating perpendicular lines. Moreover, apart from this tablet, there is no Practical evidence that this was or became a common Babylonian practice.”

According to Ossendrier, the Si.427 and Plimpton 322 clay plates are therefore peculiar. “This differs from other Babylonian mathematical practices, which apprentice scribes learned from their teacher, and which left their mark in many places in Mesopotamia in the form of school-exercise tablets or tablets for wiping practice.”

Pronin: Foundations of Science, The Guardian, New Atlas