When most people think of shapes, they imagine a triangle, a rectangle, or maybe even a fancier-sounding rhombus or trapezoid. But to mathematicians, shapes encompass a vast universe of surprising ...

Scheme illustration of object identification and all-optical 3D reconstruction system. (a) A contour surface image of the object can be obtained in a single processing of the system. (b) High-contrast ...

Can you imagine the imprint a four-dimensional hexagon might leave as it passes through your three-dimensional kitchen table? Probably not, but some people can. One such person was mathematician ...

The notion of dimension at first seems intuitive. Glancing out the window we might see a crow sitting atop a cramped flagpole experiencing zero dimensions, a robin on a telephone wire constrained to ...

The basic lantern object is made by cutting a polymer sheet into a diamond-like parallelogram shape, then cutting a row of parallel lines across the center of each sheet. This creates a row of ...

Mathematicians are “reinventing the wheel” by giving it a new shape. Their newly imagined wheel looks like a many-dimensional guitar pick, and it could theoretically roll in ways beyond our ...

The central objects of study in topology are spaces called manifolds, which look flat when you zoom in on them. The surface of a sphere, for instance, is a two-dimensional manifold. Topologists ...