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See more in our gallery: “3D printer reveals mathematical beauty – and surprise“

ARCHIMEDES was at the cutting-edge of Ancient Greek technology but he might have increased his ability to engage with ordinary folk had he access to a 3D printer.

One of the polymath’s favourite proofs was showing mathematically that a sphere that fits exactly inside a cylinder fills two thirds of its volume. A representation of this was displayed on his tomb.

Now, to mark the 2300th anniversary of his birth, Elizabeth Slavkovsky and Oliver Knill of Harvard University have used a 3D printer to create an object of the precise dimensions needed to demonstrate the insight visually.

They printed a slightly different version of the proof – a hollow hemisphere supported above a cylinder which contains a cone that takes up one third of the cylinder’s volume (pictured). Fill the hemisphere with water and it drains into the cylinder, filling it exactly to the brim. Using a hemisphere means you can see the water drain, making it easy to grasp what Archimedes proved ().

The pair reckon that 3D printers – which make it easy to create objects based on equations – could transform mathematics education. Slavkovsky has helped students print personalised mathematical objects. “It gave them a tangible thing to consider,” she says.

This article appeared in print under the headline “3D-printed proof of Archimedes”