Did you ever screw up your homework so badly that it gets preserved in stone and analyzed by researchers thousands of years later? Well, someone in Babylon did.
The artifact in question is a small, round clay tablet measuring approximately 3.2 inches (8.2 centimeters) in diameter. Unearthed from the archaeological site of Kish in modern-day Iraq, this tablet is now housed in the Ashmolean Museum at the University of Oxford. It stands among roughly two dozen similar tablets, all believed to be the remnants of ancient Babylonian mathematics education.
The clay tablet is written in cuneiform, a writing system used in several languages of the Ancient Near East. The task was essentially to calculate the area of a triangle. The student was given the height of the triangle (1.875) and the base (3.75). Can you solve the problem?
To get the of the triangle, you multiply the base and the height and divide them by 2. So, you have:
(1.875*3.75)/2 = 3.515625.
The number is long, but the formula is pretty straightforward. The Babylonian student, however, got 3.1468 — the wrong solution. The error appears to have arisen through misplacing the sexagesimal place of one part of an intermediate calculation, researchers from the Ashmolean note.
Babylonian mathematics was notably advanced for its time. They employed a base-60 number system, a vestige of which persists today in our measurement of time — 60 seconds in a minute, 60 minutes in an hour. Remarkably, Babylonian scholars understood the Pythagorean theorem more than a millennium before Pythagoras, recognizing that the sum of the squares of a right triangle’s two shorter sides equals the square of the hypotenuse.
Why these tablets are so interesting
The durability of clay tablets has ensured that these ancient records survive to this day, offering important insights into early human civilization.
The student’s miscalculation is trivial in itself, but it holds substantial historical significance. It shows how the ancient Babylonians transitioned from oral to written knowledge transmission, a shift that began around 3500 B.C. in Kish. This move towards documentation allowed for the preservation and dissemination of knowledge, laying the foundation for future educational systems.
Moreover, the error humanizes the ancient student. We’ve all made mistakes in school, and this reminds us that the learning process, with its trials and mistakes, is a timeless aspect of human development. It’s a direct link between modern and ancient society, one of the things that hasn’t changed. We all struggled at times with mastering mathematics.
Challenging problems
The problems the Babylonians were trying to solve in this educational system were not particularly simple. Take, for instance, the “reeds per rod” problem.
The problem involves calculating the length and area of a field based on a decreasing slope pattern. In this problem, the width of the field is specified as 1 rod (approximately 5 meters), and a slope or “furrow” decreases by 0.06 rods for every unit length, which translates to a progressive decrease in width. To solve it, the student first determines how many reeds (a smaller unit of length, approximately 2.7 meters) fit into the rod. They then calculate how much each furrow decreases in length and ultimately derive the total length of the field. Finally, the area is computed by multiplying half the width by the calculated length.
The 4,000-year-old clay tablet from Kish not only reveals an ancient student’s mathematical mistake; it opens a window into the educational systems, mathematical advancements, and cultural developments of the time. It serves as an important reminder of the universality of learning and the shared human journey towards knowledge. These tablets bridge the millennia between the ancient and modern worlds.
