In quantum mechanics, the geometry of quantum states has emerged as a powerful framework for understanding phenomena ranging ...

Cycling culture is full of little idiosyncrasies. Some of them we love and respect, like the fact that a water bottle is a ...

Nearly seven years since its last major content update, Geometry Dash received a massive update just before the holidays. Now, players are using features newly added to the game's level editor to ...

Granular metamaterials made of staple-shaped entangled particles interlock into load-bearing structures without adhesive, ...

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 ...

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 ...

Geometry may be one of the oldest branches of mathematics, but it’s much more than a theoretical subject. It’s part of our everyday lives, says Professor Jennifer Taback, and key to understanding many ...

Bike manufacturers have a bit of a tinkering habit. New models of our favorite bikes come out laden with the latest tech and adorned in splashy new colors every year. While those features are the ...

We describe a method for designing freeform optics based on the aberration theory of freeform surfaces that guides the development of a taxonomy of starting-point geometries with an emphasis on ...