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 ...

In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space. When you gaze out ...

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 ...

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 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,” ...

Recently, an international team of four, that includes Cheriton School of Computer Science professor Dr. Craig Kaplan, discovered a single shape that tiles the plane—an infinite, two-dimensional ...

In one of the most memorable interviews of my career thus far, I was at my desk, head in my hands, talking on the phone to a physicist about extra dimensions. I was trying to understand what it means ...