One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire ...

Q We moved into an Eichler home in Palo Alto that was built in the early 1950s. We have two concerns. The gaps between some of the ceiling boards are as large as 9/16" and we can see something black ...

Proving the “discrete” periodic tiling conjecture for high-dimensional lattices is a slightly different problem than proving the continuous version of the conjecture, as there are tilings that are ...