A 3,700-year old Babylonian clay tablet reveals an ancient method of constructing right-angled triangles that makes it the world’s oldest and most accurate trigonometric table.
The ancient Babylonians – who lived from about 4,000BCE in what is now Iraq – had a long forgotten understanding of right-angled triangles that was much simpler and more accurate than the conventional trigonometry we are taught in schools.
Our new research, published in Historia Mathematica, shows that the Babylonians were able to construct a trigonometric table using only the exact ratios of sides of a right-angled triangle. This is a completely different form of trigonometry that does not need the familiar modern concept of angles.
At school we are told that the shape of a right-angled triangle depends upon the other two angles. The angle is related to the circumference of a circle, which is divided into 360 parts or degrees. This angle is then used to describe the ratios of the sides of the right-angled triangle through sin, cos and tan.
But circles and right-angled triangles are very different, and the price of having simple values for the angle is borne by the ratios, which are very complicated and must be approximated.
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