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 ...

Researchers have discovered a hidden quantum geometry inside materials that subtly steers electrons, echoing how gravity warps light in space. Once thought to exist only on paper, this effect has now ...

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 ...

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 ...

A road bike frame is essentially three big tubes stuck together in a triangle, four thinner ones to support the rear wheel and a fork to hold the front wheel and allow it to turn. But it’s a lot more ...