The Babylonians had a long lost understanding of right-angled triangles that was simpler and more accurate than the conventional trigonometry.
The new research shows that the Babylonians construct a trigonometric table using the correct ratios of sides of a right-angled triangle. It is a completely different form of trigonometry that does not need a modern concept of angles.
We know that the right-angled triangle depends upon the other two angles. The angle related to the circumference of a circle, which divided into 3600. This angle used to describe the ratios of the sides of the right-angled triangle through sin, cos and tan.
However, circles and right-angled triangles are different, and the price of simple values of the angle is borne by the ratios, is very complicated and must be approximated.
The Babylonians discovered their own trigonometry during 1900-1600 BCE. The trigonometry contains none of the hallmarks of our modern trigonometry. It does not use angles and approximation.
The Babylonians had a completely different conceptualization of a right triangle. Their sophisticated sexagesimal (base 60) number system constructs a wide variety of right triangles using only exact ratios. They generate a wide variety of right-angled triangles with exact ratios of b/l and d/l, where b, l and d, are the short side, long side and diagonal of a rectangle.
Plimpton 322 tablet
Plimpton 322 written between 1822-1762 BCE. Philanthropist George Arthur Plimpton bequeathed his collection of mathematical artifacts to Columbia University in 1936, and it resides there today in the Rare Book and Manuscript Library.
In 1945, the tablet reveals a higher sequence of integers that satisfy the Pythagorean equation. Fundamentally a trigonometric table describes with three ratios of a right triangle. The ratio replaces tan would then b/d or d/b, but neither expressed exactly in sexagesimal.
The most worthy feature of Babylonian trigonometry is its precision. Babylonian trigonometry is exact, whereas we accustomed to approximate trigonometry.
The Babylonian approach is also much simpler because they use exact ratios. There are no irrational numbers and no angles, and also no sin, cos or tan or approximation.
Researchers say, it is difficult to say why this approach to trigonometry has not survived. The Greek approach using angles is suitable for astronomical calculations. We are only beginning to understand this ancient civilization, which is likely to hold many more secrets waiting to be discovered.
More information: [Science Direct]