From math puzzle to quantum physics gamechanger: 3D shapes that retrace almost any path

“Some shapes roll in a straight line, some roll in a curve, and some shapes roll in peculiar and seemingly surprising ways.

“But what if I told you that the strange swaying of this particular shape is not as unpredictable as it seems? In fact, this shape has been designed to follow a very specific path. According to new research, for almost any path that you care to draw, a shape theoretically exists that can follow it.”

See how researchers from the Institute for Basic Science’s Center for Soft and Living Matter and the University of Geneva worked out the physics—forms, weight, sharp corners, slopes, materials, friction, and more—of creating 3D plastic shapes that would follow predetermined routes as they rolled.

This Nature video reviews how these solid-body ‘trajectoids’ were shaped to roll along desired pathways and the complex mathematical algorithm behind their creation.

Plus: What started out as a playful math challenge soon became a powerful mathematical puzzle that might help physicists gain fresh insights into the mysteries of the quantum realm—a subatomic world where particles like electrons and photons behave in ways that often defy classical physics.

“Quantum states are often represented as points on the surface of a sphere, with a change of state being equivalent to a path across that surface. It’s possible that this quirky mathematical discovery could be applied to quantum computing or quantum optics.

“But regardless of that, right now these researchers are happy to have shown something no-one else has before: a mathematical principle demonstrated in the real world, with a whole host of surprising rolling shapes.”

Watch these related videos next:
• Physical models of abstract math: How Round Is Your Circle?
• Never-Ending Blooms: John Edmark’s spiral geometries
• Three Gears are Possible
• The Sphere-Packing Problem
• An accidental toy inventor’s shapeshifting designs
• The Hypercube: Projections and Slicing (1978), an animated tour of a 4-dimensional cube
• Denys Fisher, Inventor of the Spirograph (1977)