Imagine a universe where you could point a spaceship in one direction and eventually return to where you started. If our universe were a finite donut, then such movements would be possible and ...

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 ...

Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about. In the early 1800s, William Rowan Hamilton discovered a new kind of ...

Anyone interested in astronomy realizes that the stars are scattered through three-dimensional space and not, as the ancients thought, points of light affixed to a celestial sphere. The night sky has ...

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,” ...