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

Quantum geometry describes quantum states in systems with changing system parameters, such as an electron spinning in a magnetic field whose direction is slowly changing. The state of the electron ...

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 ...

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

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 ring in space, at least on paper, can do something a black hole cannot. It can connect distant regions without forcing ...

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 ...

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

Quantum materials can be loosely defined as materials for which quantum mechanical effects manifest on a macroscopic scale. Two classes of quantum materials are paradigmatic: superconductors, and ...

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 ...

Now, though, it’s the turn of the Seka Spear, a bike (or frameset, I should probably say) that has been at the very forefront ...

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 ...