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 ...

Scientists have created a new technology to assemble matter in 3D. Their concept uses multiple acoustic holograms to generate pressure fields with which solid particles, gel beads and even biological ...

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 cosmos seems to have a preference for things that are round. Planets and stars tend to be spheres because gravity pulls clouds of gas and dust toward the center of mass. The same holds for black ...

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 ...

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 ...

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 ...

The book Flatland: A Romance of Many Dimensions by Edwin A. Abbott explores the concept of physical dimensions through characters who encounter higher-dimensional beings. The protagonist, “A. Square,” ...

Scientists from the Max Planck Institute for Medical Research and the Heidelberg University have created a new technology to assemble matter in 3D. Their concept uses multiple acoustic holograms to ...