A recent discovery suggests that the Pythagorean theorem could be the oldest known case of plagiarism in the world.
To the ancient Greek philosopher, born in 570 BC. C., he is credited with creating mathematics that helps find the missing side of a right triangle.
But a modern mathematician discovered an ancient Babylonian tablet with the concept that predates the birth of Pythagoras by more than 1,000 years.
The evidence was translated from a clay tablet labeled YBC 7289, formed between 1800 and 1600 BC. C., which uses principles of the Pythagorean theorem to calculate the length of a diagonal within a rectangle.
Experts believe that the ancient Greek philosopher may have heard about the theorem from word of mouth and popularized it, but he still made it his own.
A modern mathematician discovered an ancient Babylonian tablet with the concept that predates the birth of Pythagoras by more than 1,000 years. The evidence was translated from a clay tablet labeled YBC 7289 (pictured).
Legend has it that Pythagoras discovered “his theorem” in the hall of a palace.
When he was bored, he would study the square stone mosaics and imagine right triangles within the mosaics.
He recognized that the area of the squares of the side lengths was equal to the square of the hypotenuse.
From this observation, he believed that the same would be true for right triangles of different side lengths. Some time after this experience, he arrived at the proof of his theorem by the deductive method.
Mathematician Bruce Ratner, who conducted the research, has a Ph.D. in Mathematical Statistics and Probability from Rutgers University.
He wrote: “There is concrete evidence (not Portland cement, but a clay tablet) that indicates indisputably that the Pythagorean Theorem was discovered and proven by Babylonian mathematicians 1000 years before Pythagoras was born.”
ratner published the study in the Journal of Targeting, Measurement and Analysis for Marketing in 2009, but the work has since resurfaced online.
Ratner analyzed the YBC 7289 tablet found in southern Mesopotamia and preserved at Yale University.
The tablet has etched markings throughout, showing a tilt square and its two diagonals, with some engraved marks along one side and below the horizontal diagonal.
The tablet was formed between 1800 and 1600 BC. The reverse is pictured.
The tablet has etched markings throughout, showing a slanted square and its two diagonals, with some etched markings along one side and below the horizontal diagonal.
Ratner plotted numbers by translating them from base 60, the counting system used by the ancient Babylonians.
Base 60, also known as sexagesimal, is a number system that uses 60 as a base instead of the more common base 10 (decimal) that we use in our daily lives.
In a base 60 system, numbers are represented using 60 different symbols or digits, much like we use the digits 0 through 9 in our decimal system.
It is used to measure time, plot coordinates and a concept of trigonometry.
‘The number at the top left is easily recognized as 30,” the study reads.
Legend has it that Pythagoras discovered ‘his theorem’ in the hall of a palace
‘The number immediately below the horizontal diagonal is 1; 24, 51, 10 (this is the modern notation for writing Babylonian numbers, in which commas separate the sexagesion ‘digits’ and a semicolon separates the integral part of a number from its fractional part).
‘By writing this number in the base 10 system, you get 1+24/60+51/60+10/60= 1.414213, which is nothing other than the decimal value of the square root of 2, to the nearest hundred-thousandth of precision.’
Ratner stated that “the conclusion is inescapable.”
He went on to explain in the study that there are two tablet-related factors that are “particularly significant.”
The first is that the marks prove that the Babylonians knew how to calculate the square root of a number with remarkable precision.
The unknown creator of the tablet understood a simple method of calculation almost 4,000 years ago: multiply the side of the square by the square root of two.
“But one question remains unanswered: Why did the scribe choose side 30 for his example?” Ratner wrote.
‘The 30 was probably used for convenience, as it was part of the Babylonian sexagesimal system, a base 60 number system.
“From this is derived the current usage of 60 seconds per minute, 60 minutes per hour, and 360 (60 × 6) degrees in a circle.”