Ancient Babylonians Used Geometry to Track the Planets

The Babylonians were even more mathematically advanced than we thought. A new report published today in the journal Science concludes that the ancient people may have been using geometry to chart the movements of the planet Jupiter as early as 350 BCE— long before the 14th century, when European astronomers were thought to have pioneered the approach.

These findings are the result of years of work by Mathieu Ossendrijver, who literally wrote the book on the Babylonians’ use of math in astronomy. Ossendrijver has spent more than a decade analyzing the cuneiform markings on a set of stone tablets found in modern-day Iraq. The tablets have been sitting in the collection of the British Museum since 1881.

The Babylonians’ interest in astronomy is well established, but the calculations etched into four nearly complete tablets dating to between 350 BCE and 50 BCE are the first indication that the ancient astronomers had moved beyond simple arithmetic into geometrical concepts. The tablets' creators were focused on tracking Jupiter across the ecliptic, an invisible line that roughly represents the path of the Sun. They based their calculations on a trapezoid’s area, and its “long” and “short” sides. A newly discovered tablet dating to the same era, which has the same computation of Jupiter's movement in an arithmetical formulation, also helped solve the mystery. 

Ossendrijver’s findings represent a radical change in the timeline of astronomy. As the author writes in his report, “These computations predate the use of similar techniques by medieval European scholars by at least 14 centuries.”

The Babylonians were not the only people using geometry at that time, Ossendrijver notes, but they were the only ones using it in such an advanced manner. Greek astronomers like Aristarchus of Samos, Hipparchus, and Ptolemy incorporated geometry into their calculations, but limited their calculations to physical space. Babylonian calculations were more abstract and sophisticated, taking into consideration both velocity and time—an advancement that allowed them to accurately predict the movements of Jupiter along the ecliptic.