A mathematician from Australia has found what could be the oldest example of applied geometry on a Babylonian clay tablet that dates back to 3700 years.The tablet is also known as Si.427 and bears a field map that shows the boundaries of land.It dates back to the Old Babylonian period, between 1900 and 1600 BCE. It was found in Iraq in the latter part of the 19th century. The tablet was previously housed at the Istanbul Archaeological Museum until Dr Daniel Mansfield, University of New South Wales, found it.Norman Wildberger, associate professor at UNSW had previously identified a Babylonian tablet containing the oldest and most precise trigonometric table in the world. They speculated that the tablet might have been used in construction or surveying.This ancient clay tablet was engraved using a stylus to describe a marshy area, threshing floor, and tower. Photo by UNSW SydneyPlimpton 322, a tablet that was presented right-angle triangles with Pythagorean Triples, described them. It used three whole numbers, in which the sums of the squares from the first two equals to the square of third. For example, 32 + 42 = 52.Mansfield stated that trigonometry is not something you just happen to stumble upon, but rather, it's often something you do. Plimpton 322 led him on a search for other tablets that had Pythagorean Triples from the same period, which eventually led him to Si.427.Mansfield stated that Si.427 refers to a piece or land being sold. The cuneiform script with its distinctive wedge-shaped indentations describes a field that contains marshy areas as well as a nearby tower and threshing floor.According to Mansfield, the rectangles that depict the field have opposite sides and equal lengths. This suggests that surveyors at that time had created perpendicular lines with greater accuracy than ever before.Similar to today, private citizens are trying to determine their land boundaries. The surveyor arrives but instead of using GPS equipment, they use Pythagorean Triples.Although Si.427 and Plimpton 322 both use Pythagorean Triples, they are more than 1,000 years older than the Greek mathematician Pythagoras.Mansfield stated that once you have a good understanding of Pythagorean Triples, your society will be at a certain level of mathematical sophistication.Three Pythagorean triples are found in Si.427: 3, 4, 5, 8, 15, 17, and 5, 12,Babylonians used a base 60 system of keeping time, similar to the way we do today. This made it difficult to work with prime numbers greater than five.Si.427 was described in a Foundations of Science study. It dates back to a time of increasing private land ownership. Mansfield stated that now that we understand the problem that the Babylonians were trying to solve, it was possible to recolour all of the mathematical tablets from that period. Mathematics is being used to meet the current needs.Mansfield is puzzled by Si.427's sexagesimal numbers 25:29 and 25 minutes 29 seconds, which are etched in large fonts on the tablet's back.Does it belong to a calculation they did? Is this an area I haven't yet found? He said that it was a measurement of some thing. It's annoying because I don't understand so much about this tablet. I've given up trying and figure it out.
