Changing light's polarization can reverse the structure of a patterned light field, opening a new way to control geometry and information in optics. (Nanowerk Spotlight) Light can be bent, focused, or ...

Materials were written for an entire year's course in geometry in which transformations were used to develop the concepts of congruence, similarity, and symmetry, as well as being a vehicle for proof.

In an era driven by complex data, scientists are increasingly encountering information that doesn't lie neatly on flat, Euclidean surfaces. From 3D medical scans to robot orientations and AI ...

Geometric objects take on different properties depending on the space in which you visualize them. Using techniques from an upstart field called tropical geometry — which analyzes complicated shapes ...