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 ...

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,” ...

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 ...

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 ...

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 dealing with higher dimensions in geometry, it is often instructive to start with lower ones and work your way up. If we start with two points, which are by definition each of zero dimension, we ...