Did Babylonians Discover Trigonometry 1000 Years Before the Greek?
The dominant archeological perspective gives us a good baseline as to what our ancient ancestors knew, but every so often a discovery comes along that challenges those theories. We can thank the late, great journalist George Plimpton for one artifact that has recently challenged that narrative, potentially setting back the history of mathematics and casting a new light on the ever-intriguing culture of the ancient Babylonians. That artifact known as Plimpton 322, is a cuneiform tablet that was purchased almost a century ago from the real-life Indiana Jones, and could potentially prove that the ancient Babylonians were the first civilization to understand trigonometry.
Cuneiform Tablets
Pythagoras is thought to have been the first to understand that the area of the square of the hypotenuse of a right-angled triangle is equal to the sum of the areas of the squares of its other two sides, a.k.a. the Pythagorean theorem. But it’s not necessarily well-documented that Pythagoras actually conceptualized this equation, nor are any other of his mathematical achievements.
Pythagoras ran a school that was shrouded in mystery and secrecy, with a kabbalistic take on math and numbers. Some believe it is possible that his students may have been responsible for his supposed achievements in mathematics but, due to either reverence or fear, gave credit to Pythagoras. Interpretations and documentation from the time are scarce, as knowledge was typically spread by word of mouth. At the same time, Pythagoras’ school was almost cult-like with stories of members being murdered for not maintaining the school’s secrecy and learnings.
The ancient Babylonians, on the other hand, used cuneiform tablets to record much of their intellectual work, with thousands of tablets having been recovered to this day. Many of them were excavated in the early 1900s and sold to museums or collectors, but some of the implications of their carvings are challenging what archeologists have believed about ancient history. One of these tablets was purchased by George Plimpton for a mere $10 in 1922 and has been the center of heated debate between archeologists. The new theory pairs the findings from Plimpton 322 with another tablet, known as YBC 7289, and posits that Babylonian mathematics included trigonometry, predating the Greek by 1,000 years. These ancient Babylonians used a base-60 system of mathematics rather than the base-10 system that we use today.
Plimpton 322 – wikipedia.com
While we have all assumed Pythagoras to be the first to postulate his eponymous theorem, Hipparchus is generally thought to be the Greek father of trigonometry and the first to produce a trigonometric table, known as the table of chords. Hipparchus’ work required a knowledge of trigonometry for measuring astronomical distances, but much of the basis for his work came from Babylonian mathematics using the base-60 system. Also, few details are known specifically about his life, despite being credited with the discovery of a large field of mathematics.
The base-60 system allowed the Babylonians to make trigonometric calculations in terms of ratios rather than angles. What is so fascinating about this discovery is that it brings a subjective interpretation to mathematics, which may seem counterintuitive. But the ancient Babylonian system of trigonometry shows that they were capable of achieving similar results using a different mathematical perspective. Part of their base-60, or sexagesimal system, is even retained today in certain elements of our lives like the number of seconds in a minute, the number of minutes in an hour, and the number of degrees in a circle.
Cuneiform Translations
Plimpton 322 was dated between 1822-1762 BC, around the rule of King Hammurabi, and contains a reference chart with four columns and 15 rows, laying out a table of ratios of right-angled triangles. These triangles range in proportion from nearly a square to a near flat line. The table is thought to have been used for construction purposes and could provide insight as to how the ancient Babylonians were such skilled architects and engineers. The ziggurats, hanging gardens and novel urban planning of the ancient culture are signs of a mathematically adept civilization, so it should be unsurprising that they could have been the first to develop trigonometry.
Cuneiform is the oldest written language in the world, created by ancient Mesopotamian civilizations using wet clay that was etched into and then baked in the sun or ovens. Written in either Akkadian or Sumerian, the majority of these tablets were excavated by Edgar J. Banks who was an archeologist and antiquities dealer, also thought to be the archetype for the character of Indiana Jones. Banks is thought to have uncovered and sold thousands of cuneiform tablets toward the end of the Ottoman Empire. The one sold to Plimpton however, has been one of the most controversial, regarding its implications on the history of trigonometry, while thousands of other tablets remain in private collections and museums that could shed further light on the subject.
Plimpton 322 was excavated in what would have been the ancient city of Larsa and was originally thought to be a scribe’s tally sheet or inventory report for transactions at a marketplace. If the cuneiform translations of Plimpton 322 as a trigonometric table are true however, they would not only change the study’s provenance, but also be considered the world’s oldest completely accurate trigonometric table. If this is true it would add yet another layer of profound sophistication to an already oddly advanced ancient civilization.
About the Author
Exploring the Ancient Pyramids of the World
If there is one structure that still gives rise to great amounts of interest, speculation and awe, it’s the ancient pyramids.
Oftentimes when we think of the pyramids, we concentrate our attention on the most famous –– the Egyptian pyramids so often featured in movies and travel magazines.
But there are actually many more pyramid locations other than Egypt, including Central America, China and beyond. You may be surprised by the varied places you can find pyramids across the world –– including underwater.
By delving into more pyramid facts, we can unlock more information and understanding about these sizable structures, their prominence throughout the world, and even their relevance for those throughout the world.
What Exactly is a Pyramid?
While you may have initially learned about the pyramid shape in geometry class, architectural pyramids are a bit more complex.
Generally the shape of pyramids include at least three outer triangular surfaces which join together at a point at the top, with the base being any number of shapes with multiple sides. This means that the base of a pyramid could be a square or other polygon.
Pyramids were generally built this way in order to distribute the majority of the weight closer to the ground, meaning less pressure coming from the top. This also allowed the builders of the pyramid to more easily constrict the structures using dry stone construction.
Pyramids in Ancient Civilizations
While the general pyramid structure generally remains the same, each civilization that constructed pyramids did so in a slightly different way. Let’s take a look at a few of the civilizations that lay claim to impressive ancient pyramids, and why each one is worth a closer look.
Egypt
The three famous ancient pyramids found in Egypt are what most people think of when they think of the pyramids. Current Egyptologists believe the Great Pyramid was constructed for Pharaoh Khufu, and is situated the furthest north.
Said to have been constructed in 2551 B.C., it used to measure about 147 meters, it now stands at around 137 meters, and contains more than 2 million blocks. The Great Pyramid was deemed one of the Seven Wonders of the World by the Greeks, and is the only one that has survived to the present day.
Another one of the over 100 pyramids in Egypt is the Pyramid of Djoser, built for his namesake the Pharaoh as a mausoleum. This pyramid is more of a step pyramid design, which involved six successively smaller layers and a flat top.
