Apr 16, 2016 | By Tess

Roughly 3,800 years ago, during the Old Babylonian Period, students did not sit around chalkboards or calculators to learn the principles of math, in fact, many of the principles of math we now have in books were not even yet discovered. An ancient artefact dating from that period, however, has shown us that though the people of the Old Babylonian Period existed over a thousand years before Greek geometer Pythagoras coined the “Pythagorean triangle” principle, they still understood the mathematics behind it. The ancient geometry tablet, which has been part of Yale University’s Babylonian Collection since it was donated as part of a larger collection of cuneiform tablets in 1909, is now being reintroduced into classrooms and to the public thanks to 3D scanning and 3D printing technologies.

The circular tablet, made from clay, was made sometime between 1,900 and 1,700 B.C.E. and is inscribed with a diagram and numbers that indicate that the basic principle of the Pythagorean Theorem was already understood. The diagram also reportedly demonstrates that the people of Old Babylonia were capable of calculating the square root of 2 up to an accuracy of six decimal places. Of course, the numbers and inscriptions do not bear resemblance to our own, but are represented through pictographic symbols made by pressing a sharp stylus into the surface of the fresh clay.

“This geometry tablet is one of the most-reproduced cultural objects that Yale owns — it’s published in mathematics textbooks the world over,” says Professor Benjamin Foster, curator of the Babylonian Collection. “At the Babylonian Collection we have a very active teaching and learning function, and we regard education as one of the core parts of our mission. We have graduate and undergraduate groups in our collection classroom every week.”

Of course, being nearly 4,000 years old, the clay tablet is fragile and cannot be physically handled by a number of people without suffering damage. So, like with many other tactile artefacts ancient artefacts, Yale University opted to 3D scan and reproduce the geometric learning tablet with 3D printing technologies. To digitally render the geometric tablet, the Babylonian collection’s curators partnered with experts at Yale’s Institute for the Preservation of Cultural Heritage (IPCH).

Before 3D scanning the tablet (and 13 other artefacts from the collection), the team at IPCH first conducted a process of reflectance transformation imagine (RTI), a photographic technique that uses various lighting angles to provide a number of different perspectives and literally sheds light onto subtle surface variations more than any static photo could. With the information from the RTI collected, two of IPCH’s members, Chelsea Graham and Yang Ying Yang then laser scanned the tablet to generate a 3D model of the educational artefact.

With a manipulatable digital rendering of the model, the IPCH then reached out to Yale’s Center for Engineering Innovation and Design which has collaborated with them in the past to additively manufacture objects and various historical artefacts. Joseph Zinter, the center’s assistant director says of the importance of physically holding an artefact, “Whether it’s a sculpture, a rare skull, or a microscopic neuron or molecule highly magnified, you can pick up a 3D printed model and hold it, and it’s a very different and important way to understand the data. Holding something in your hand is a distinctive learning experience.”

That is, while the 3D digital model of the tablet is itself ripe with information and can be explored, the tactile qualities of the 3D printed 3,800 year old geometric tablet will provide people, and especially students with an additional understanding of how ancient populations used to learn.

Graham, who helped digitally scan the artefact, says, “It strikes me that this tablet has made a very long journey from classroom to classroom. People sometimes think the digital or 3D-printed models are just a novelty, or just for exhibitions, but you can engage and interact much more with the 3D printed object, or 3D model on the screen. I think the creators of this tablet would have appreciated the efforts to bring this fragile object back to the classroom.”

Currently, a team from the IPCH is working on creating an “integrated collaborative software platform” to efficiently share digital files of cultural artefacts across many schools and institutions. Ultimately, they are hoping to create one virtual environment that can connect a number of different media and streamline all of a project’s documents and information. Having a large digital collection of artefacts will not only make them more accessibly, but also allow researchers to make new comparisons and analyses between various objects from collections around the world.



Posted in 3D Printing Application



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