Mathematical Artifacts

Plimpton 322. Image: Public domain, via Wikimedia Commons.

Plimpton 322. Image: Public domain, via Wikimedia Commons.

Plimpton 322 is a historical math document displaying Babylonian mathematics on a clay tablet. I had never heard of such a tablet or seen an artifact similar to Plimpton 322. From watching the documentary in class on Plimpton 322, I had learned that it was a tablet with a list of Pythagorean triples. The tablet was discovered somewhere unknown in Iraq. Plimpton 322 is similar to math that we study today. It displays a numeric with a different base. I began to wonder what other historical mathematical artifacts had existed around the world and how they were used in their societies. Also what were the similarities and differences when comparing them to the Plimpton 322? Studying and learning about historical math artifacts can reveal our math heritage and explain why we learn and need math.

To start understanding how math was used thousands of years ago , we can go back to southern Africa in 35,000 B.C. One of the oldest mathematical artifacts that has been discovered in the world is the Lebombo bone. The bone was a baboon’s fibula bone with 29 markings that are believed to represent a lunar calendar. This bone was found in a cave in Lebombo, between South Africa and Swaziland. The bones were marked with important figures that recalled events yearly. Similar to the Plimpton 322, symbols that had a meaning were carved on an object to create a permanent marking. The reasons these artifacts were used, though, were completely different. These bones were used to keep track of yearly events. Of course, Plimpton 322, which is more than 30,000 years younger than the Lebombo bone, was used for a more advanced purpose. It tracked and listed Pythagorean triples by using a numbered system that the Babylonians had developed.


An example of what a quipu looked like, with knots and different colors. Image: A. Davey, via Flickr.

Though Plimpton 322 and the Lebombo bone used a mathematical system of markings on a surface to represent something significant to them, other cultures created artifacts that did not require anything to be written down. I came across the Quipu, which according to April Holloway is “the ancient mathematical device of the Inca.” The quipu is different from Plimpton 322 and Lebombo bone because it shows that mathematics doesn’t have to be written down to be significant. It was discovered in the valley of Canete close to Lunahuana, Peru. This device stands out because this Inca artifact was created out of various material that includes: llama or alpaca hair or cotton cords. These strands were colored, spun and plied. Maybe you are wondering, how did this artifact use math and how was it used in its society? April Holloway states that the strands “contained numeric and other values encoded by knots in a base ten positional system.” There was no limit on the number of cords each quipu could have had. Quipus ranged from having a few to 2,000 strands. The color, the amount knots, and the type of material used, all represented something specific to the Inca society because it was “both statistical and narrative information.” There have been 200 found but they are not older than 650 A.D. and because these artifacts are not as old, there is more information known about the quipus. Besides the 200 that were found, the Spanish conquistadors destroyed a lot of the quipus. Though the quipus were used to collect data, document census records, calendrical information, military organization, etc., the Spanish conquistadors thought of the quipus as something that represented the Inca religion. April Holloway claims in her article that, “the conquistadors were also attempting to convert the indigenous people to Roman Catholicism. The Inca religion was considered idolatry, anything that represented or was used by them was an attempt to disregard Catholic conversion.” Unlike the previous artifacts, a lot is known about the quipu and a lot of different samples were found showing the variation among them.

We learn and need math for many reasons, and societies develop systems to represent their idea of mathematics. The three artifacts that I found and learned about (including Plimpton 322), were completely different in how they were created and what they were created for. The oldest artifact that has been found is the Lebombo bone from 35,000B.C. It used a method of carving lines (the bone had 29 lines carved on it.) One of the oldest mathematical systems is still used today to teach children how to count. Thousands of years later in 1800 B.C., Plimpton 322 was created. Plimpton 322 was advanced compared to the Lebombo bone. It used a numeric system which expressed Pythagorean triples. The numeric system on the tablet was represented by symbols and used a base 60. Similar to the Lebombo bone, it had a system of math written on the artifacts. The most interesting and different artifact was the quipu which were created around 650 A.D. It is not similar to any math system that we use today. Every detail (like the material and color) about the quipu represented something significant. There are possibly many other mathematical artifacts in the world. How they were created and how they were used in their societies reflects how math was something civilizations have always needed. Artifacts, like the Lebombo bone, Plimpton 322, and the Quipu, reflect how they each could have shaped and develop the math that we used today.

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