For decades mathematicians have searched for a specific pair of surfaces that can’t be transformed into each other in four-dimensional space. Now they’ve found them. In geometry and the closely ...

Yes, it is possible to create a three-dimensional image of a four-dimensional object: a hypercube is the four-dimensional analogue of a cube, and it has a well-known three-dimensional image that looks ...

In the illustration: A tesseract (a four-dimensional cube) and the "shadow" it casts on a plane—the quasicrystal discovered by Shechtman. According to Prof. Bartal, "The fact that a quasicrystal is a ...

When you are sent to do a bit of work experience in the office of a university science department you don’t normally expect much more than a bit of boring filing and some tedious photocopying. So ...