It can be tempting to assume that your intuitions about three-dimensional space carry over to higher-dimensional realms. After all, adding another dimension simply creates a new direction to move ...

New work on the problem of “scissors congruence” explains when it’s possible to slice up one shape and reassemble it as another. If you have two flat paper shapes and a pair of scissors, can you cut ...

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 ...

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 ...