Geometry

MIT researchers have solved a geometry problem that explores how to divide n-dimensional spaces into theoretically equal “slices," reports Juandre for Popular Mechanics. “I can tell you at the beginning, we were a little bit stuck. We made some partial progress, but I guess by hitting those roadblocks we just learned a lot about what we needed at the end,” explains Zilian Jiang, a former Applied Mathematics Instructor at MIT. “That was [a] great experience, because at least for me personally, I feel like doing research is also about the experience.”

New research by Professor Erik Demaine, lecturer Zachary Abel, robotics engineer Martin Demaine and their colleagues explores whether it is possible to “take any polyhedral (or flat-sided) shape that’s finite (like a cube, rather than a sphere or the endless plane) and fold it flat using creases," writes Rachel Crowell for Quanta Magazine. “By moving finite to infinite ‘conceptual’ slices, they created a procedure that, taken to its mathematical extreme, produced the flattened object they were looking for,” Crowell explains.

In an article for The New York Times exploring whether humans are the only species able to comprehend geometry, Siobhan Roberts spotlights Prof. Josh Tenenbaum’s approach to exploring how humans can extract so much information from minimal data, time, and energy. “Instead of being inspired by simple mathematical ideas of what a neuron does, it’s inspired by simple mathematical ideas of what thinking is,” says Tenenbaum.