Some shapes roll in a straight line. Some roll in a curve. Can you make a shape that will roll in such a way as to create any path you care to draw?
Mathematicians have come up with a way to create the shapes that roll in such a way as to create any path.
First you transfer the squiggle to the surface of a sphere. If you connect the starting point to the ending point, the pattern can repeat, but some patterns have to be drawn twice in order for it to be possible for the ends to meet.
After that, the obvious thing to do is 3D print the shapes, but in the non-theoretical non-perfect real world, some things are difficult including sharp corners and paths that cross over themselves, and if the friction isn't right between the object and the surface, the shapes don't roll properly.
These shapes roll in peculiar ways thanks to new mathematics - nature video
