The polytope framework suggests an answer: identity isn't located in any particular plank but in the geometric constraints that govern how planks relate to each other. Change any component, but if the ...

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.