![]() A seventh triangle causes the plane to wrinkle-moving it out of Euclidean space and bestowing a doily-like texture. Laid flat on a table, you’d only be able to fit six of these triangles around a shared point. It is made from dozens of hinged, equilateral triangles. “And it’s not like you can just go to the store and buy yourself a pentagonal hexecontahedron.” Taalman remembers going to the hardware store and scavenging for scraps of string and dowels to make her models of complex knots and hinged surfaces.Ībove all, Segerman delights in using shapes to explain mathematical concepts that are incomprehensible without an advanced degree. “Mathematicians tend to think about objects that can be difficult to visualize, that are in more than two dimensions, and whose physical structure, arrangement, and symmetries are really vital to the understanding of the object,” says Laura Taalman, a mathematician at James Madison University who just finished a two-year leave consulting for the 3-D printing industry. The book’s chapters explain geometric concepts like symmetry and curvature using intricate 3-D shapes (which you can order to examine for yourself from the 3-D printing company Shapeways).īefore 3-D printing, mathematicians had to resort to plaster molds or carving wood if they wanted a physical representation of a shape. Using math, which he translates into code for a 3-D printer, he creates physical representations of everything from circular paraboloids to hyperbolic honeycombs, some of which appear in his new book Visualizing Mathematics with 3D Printing. I want to hold it in my hand,” says Segerman. When trying to study a shape in 4-D space, much less 3-D, even more is lost. A digital rendering, even one you can rotate, is, after all, a just a series of 2-D images. But certain characteristics and symmetries are just not obvious until you look at a physical representation. “I can’t see in 3-D, much less 4-D,” says Segerman.įor the past couple of decades, mathematicians have increasingly relied on digital imaging to see complex shapes. He is pioneering the use of 3-D printing technology to bring rarefied geometry, like four-dimensional symmetries, out of the minds of mathematicians and into the hands of students and academics. Which is curious-because Segerman, 37, has made a career out of visualizing complex mathematical shapes. “When I try to visualize something, I don’t see anything,” he says. Segerman immediately recognized that he lives with the same limitation. ![]() It was by a programmer who had could not conjure mental images-a condition called aphantasia. Last spring, mathematician Henry Segerman found a peculiar post on Facebook.
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