It turns out that knowledge of this property of right triangles actually predates Pythagoras.
The easiest example is the set of numbers three, four, and five.
Three squared is nine; four squared is 16.
The tablet Si.427 shows the subdivision of a field in Sippar, modern day Iraq, dating from 1900-1600 BCE. (Photo: UNSW Sydney)
Added together, that makes 25, which is the square of the hypotenuse (five).
In 2018, he discovered the artifact in the collections of the Istanbul Archaeological Museum in Turkey.
Known asSi.427, the clay tablet contains a diagram and cuneiform text (an ancient system of writing).
On the back of the tablet one can see text, written in cuneiform. The text corresponds to the diagram on the front – describing the size of the field. (Photo: UNSW Sydney)
Its creator was an ancient land surveyor during the OB period of 1900 to 1600 BCE.
The markings were carved with a stylus, as was the custom of writing.
On the back of the tablet one can see text, written in cuneiform.
The surveyor managed to be so precise by using Pythagorean triples–making the boundary lines he created truly perpendicular. (Photo: UNSW Sydney)
The text corresponds to the diagram on the front describing the size of the field.
This suggested the surveyor had a mathematical method to ensure this perfection.
These could be scaled to any size as long as the ratio of sides was maintained.
Si.427 will have big implications for the history of mathematics. (Photo: UNSW Sydney)
Two triangles of the same size could also form a rectangular field.
This discovery is evidence of the first known use ofapplied geometry, over a thousand years before Pythagoras lived.
As land privatized, disputes over boundaries required sophisticated methods of demarcation and resolution.
The Babylonian number system, however, was limited.
A base 60 number system meant that the surveyor only had a limited number of useful Pythagorean triples.
Dr. Mansfield found this tablet in 2017 in the collections of Columbia University.
What is next after such a fascinating discovery?
Well, the early history of mathematics requires some serious revisions.
The surveyor managed to be so precise by using Pythagorean triplesmaking the boundary lines he created truly perpendicular.
Si.427 will have big implications for the history of mathematics.
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