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 ...

The notion of dimension at first seems intuitive. Glancing out the window we might see a crow sitting atop a cramped flagpole experiencing zero dimensions, a robin on a telephone wire constrained to ...

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 ...

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,” ...

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 ...

Three mathematicians just proved a famous 30-year-old conjecture in geometry, with only a tiny assist from AI. The conjecture says that even within enormous, scattered and chaotic assemblages of ...

Hello, I’m Mr Firth. And today we’re going to learn all about 3D films. Oh… sorry. I meant 3D shapes. I’ll save these for another time. So, what is a 3D shape? 3D is another way of saying ...