The discovery earlier this year of the “hat” tile marked the culmination of hundreds of years of work into tiles and their symmetries. Every day we see examples of repeating motifs. This symmetry and ...

Mathematicians typically appreciate either generic or exceptional beauty in their work, but one type is more useful in describing the universe. A time-honored practice in mathematical circles is to ...

Creatively tiling a bathroom floor isn’t just a stressful task for DIY home renovators. It is also one of the hardest problems in mathematics. For centuries, experts have been studying the special ...

An airplane, traveling with a constant engine speed, makes a large and perfect circle parallel to the ground. There is no wind. Will it complete the same circle in greater, less or the same time if ...