Scientists from Sydney's South New South Wales (UNSW) discovered the purpose of the famous Babylonian clay plate for 3,700 years, revealing that it is the oldest and most accurate trigonometric table in the world, probably used by ancient mathematicians to compute how to build palaces and temples and build channels.
A new study shows that the Babylonians have fought the Greeks in the Trigonometry Triangle Study for more than 1,000 years and reveals the ancient mathematical sophistication that has been hidden until today
Known as Plimpton 322, a small panel discovered at the beginning of the 20th century in today's Iraq, found by archaeologist, academician, diplomat and antique merchant Edgar Banks, a person based on whose life Indiana Jones was designed.
The board has four columns and 15 rows of numbers that are inscribed with a walnut letter using the base system 60. "Plimpton 322 confused mathematicians for more than 70 years, since it was understood to contain a special pattern of numbers called Pythagorean numbers," he said is Dr. Daniel Mansfield from the School of Mathematics and Statistics at UNSW.
"The Great Mystery, so far, was its purpose – why the ancient writers have performed a complex task of generating and sorting the numbers on the board."
"Our research reveals that Plimpton 322 describes the forms of rectangular triangles using a new type of trigonometry based on the ratio, not the angles and circles. It is a fascinating mathematical work that shows undeniable genius. "
"The board does not only contain the oldest trigonometric table in the world, but is the only fully accurate trigonometric table, because the Babylonians had a very different approach to arithmetic and geometry than the Greeks."
"This means that it is of great importance to our contemporary world. Babylonian mathematics may have been out of style for more than 3,000 years, but there are practically practical applications in geodesy, computer graphics and education. "
"This is a rare example of an ancient world that teaches us something new," he said.
A new study by Dr. Mansfield and associate professor Norman Wilderberger published in the journal Historia Mathematica, the official journal of the International Commission on the History of Mathematics
Trigonometric table allows us to use a known rectangular triangle rectangle ratio to determine the other two unknown proportions
Greek astronomer Hipparchus, who lived about 120 years before the new era, has long been considered the father of trigonometry, with its "chord tables" of the circle, considered the oldest trigonometric table.
"Plimpton 322 goes further than Hipparchus for more than a thousand years," Dr. Wilderberger said. "It opens new possibilities not only for modern mathematical research, but also for mathematical education. With the Babylonian Plimpton 322 we see a simpler, more accurate trigonometry with obvious advantages in front of our model. "
"There is the whole treasure of the Babylonian plates, but only a part of them has been studied. The mathematical world is only aware of the fact that this ancient but highly sophisticated mathematical culture has much to learn. "
Dr. Mansfield read about Plimpton 322 occasionally, while preparing materials for first year math students at New South Wales University. He and Dr. Wilderberger also decided to study Babylonian mathematics and examine the various historical interpretations of the meaning of the panel after they realized they could withdraw the paraffin with a rational trigonometry whose principle Dr. Wilderberger developed in the book "Divine Ratio: Rational Geometry to Universal Geometry."
The 15 rows on the table describe a series of 15 rectangular triangles, which are constantly decreasing in tilt.
The left edge of the board is broken and scientists base their research on previous attempts to present new mathematical evidence that it originally had 6 columns and that the board was supposed to be completed with 38 rows.
They also show that ancient writers, who used a numerical system with a base 60 that resembles our calculation of hours and times, instead of the base system 10 we use, could generate panel numbers using their mathematical techniques
Evidence was also found that contradicts the widely accepted view that the panel was helpful to teachers in verifying the solution of quadratic equations of students.
"Plimpton 322 was a powerful tool that could be used to measure surfaces or create architectural calculations for building palaces, temples and pyramids," said Dr. Mansfield.
The slab, which is believed to originate from the ancient Sumerian city of Larsa, dates from 1822 to 1762 before the New Era. It is now in the Library of rare books and manuscripts at the University of Columbia in New York.
Pythagorean numbers consist of three positive integers a, b and c such as a² + b² = c². Full numbers 3, 4, and 5 are well-known examples of Pythagorean numbers, but the values at Plimpton 322 are often considerably higher, for example, with the first order referenced to the 119th, 120th, and 169th numbers.
The name is derived from the Pythagorean rectangular triangle theorem, which states that the square of the hypotenuse (the diagonal side opposite the right angle) is the sum of squares of the other two sides.