3D Printed models have illuminated mathematical proofs from history with spherical shapes and play with light sources. Using stereographic projection, Henry Segerman and Saul Schleimer cast astounding shadows and designs from their designs. Utilizing the inverse of methods from cartographers to map the Earth, the two mathematicians designed shapes that take advantage of geometrical patterns and truths.
For a basic understanding of the process employed by the sculptures, the importance lies in the 3D shape and the light source. When the light hits the sphere from different points, like its center or an outside “infinite” space, it produces a shadow pattern, the 2D image. The angles and shapes derive from the sphere. Henry and Saul thought it would interesting to play with the order of creation and set out to make a sphere that would depict the shapes they wanted. As we have come to understand, having a physical representation of this mathematical phenomenon makes the concept tangible. This is not lost on Saul.
“Stereographic projection is a beautiful and important idea, and these models show how it works in an immediately understandable way,” says Saul. “I think people respond even better to a real-life physical demonstration than a computer animation – you can’t cheat when it’s something as simple as light and shadow!”
The mathematicians challenged themselves to come up with various patterns based on geometric proofs. They found an homage toMöbius’s famous designs and hyperbolic planes. Speaking for themselves, the designs dazzle and shift depending the light source and placement. While they can help explain math class, they can also be a new and intriguing way to illuminate your life.