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Discovery Rewrites History of Mathematics

It used to be believed that trigonometry, the study of angles, was first developed by the Ancient Greeks. While Egyptians and Babylonians certainly laid the foundations for trigonometry, the Ancient Greeks were credited with inventing trigonometry as we know it. It was believed that the Greek mathematician Hipparchus was the first to construct a trigonometric function. A discovery from Iraq has challenged this theory and may change the way we think about our history.

The Babylonians of Iraq were accomplished mathematicians. This has been known for a long time. It takes only a cursory examination of the architecture of their empire to see their mastery of geometry in their impressive ziggurats and other buildings. The Babylonians discovered zero and invented the base 60 numerical system that we still use to measure time. Now, it seems that they may have invented trigonometry one-thousand years before the Greeks were believed to do so.

The discovery was made by University of New South Wales mathematicians, Daniel Mansfield and Norman Wildberger. They found a trigonometric table on a cuneiform tablet from the Babylonian city of Larsa. The tablet was made between 1822-1762 BCE. The researchers described it as, “a trigonometric table of a completely unfamiliar kind and… ahead of its time by thousands of years.” If this discovery is true, it does explain the Babylonian skill in architecture.

What is amazing about the discovery is that the Babylonians seem to have had a deeper grasp on trigonometric concepts than we do today. They used the base 60 system rather than the base 10 system which we use. To put this in simple terms, this system’s main advantage is that it is more exact than base 10.

Mansfield and Wildberger explain it this way, “Fundamentally a trigonometric table must describe three ratios of a right triangle. So we throw away sin and cos and instead start with the ratios b/l and d/l. The ratio which replaces tan would then be b/d or d/b, but neither can be expressed exactly in sexagesimal [base 60].”

“Instead, information about this ratio is split into three columns of exact numbers. A squared index and simplified values of b and d to help the scribe make their own approximation to b/d or d/b.”

This may sound very complicated to a layman such as myself, but in essence this only means that the Babylonians had a more exact method of trigonometry. Why this system was forgotten remains a mystery. Many experts remain skeptical as to how or even if the Babylonians applied this information.


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