As Eckmann put it, the discovery shows “how rich mathematics can be even in a field as well-trod as the study of rotations.” ...

All squares have a rotational symmetry of order 4. This means that in one full rotation of 360 degrees about its centre, there are 4 positions where the shape looks identical to its starting position.

Mathematicians thought that they understood how rotation works, but now a new proof has revealed a surprising twist that ...