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,” ...

A mathematical problem solved by Susanna Heikkilä relates to the classification of quasiregularly elliptic 4-manifolds, ...

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 ...

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 ...

MADISON – When the world’s most powerful particle accelerator starts up later this year, exotic new particles may offer a glimpse of the existence and shapes of extra dimensions. Researchers from the ...

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 ...

In three-dimensional space, the surface of a black hole must be a sphere. But a new result shows that in higher dimensions, an infinite number of configurations are possible. The cosmos seems to have ...

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 ...