Physicists have engineered photons that behave as if they inhabit a space far richer than the familiar three dimensions, ...

High-dimensional spheres can have a much wider variety of structures than mathematicians thought possible. If you’ve ever been stuck in traffic on a rainy afternoon, you’ve probably watched raindrops ...

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,” ...

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 ...