Scientists Figured Out How to Design Dice to Roll Any Way You Want
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For nearly a century, mathematicians have been interested in strange shapes that hold unique mathematical properties.
One such shape is the “trajectoid,” a wonky-shaped sphere that’s algorithmically designed to followed a pre-determined path.
Further study of trajectoids could give scientists a better understanding of quantum qubits and give engineers a new tool for designing robots to travel on a set trajectory.
Ask any Dungeons and Dragons player: dice rolls don’t always go your way. But what if you could use a complex algorithm to design dice to physically roll any way you wanted?
Scientist Yaroslav Sobolev at the Institute for Basic Science in Ulsan, South Korea—along with his colleagues—have designed an algorithm that creates wonky-shaped objects called “trajectoids” that mathematically travel along any set path. The results of the study were recently published in the journal Nature.
“For any path, you can always find such a sphere, of some radius, that when it completes two periods of the path, it will restore its 3D orientation perfectly,” Sobolev tells New Scientist. “This allows you to make a particle that will roll forever downhill, always tracing the path again and again.”
The algorithm works by tracing a moldable sphere’s contact points with the ground as it travels a predetermined path. The team then created a 3D printed shell to cover the hard metal interior and tested the results against the mathematically designed path. The trajectoids followed the designed path and even successfully repeated the path twice in most cases. (If you’re a 3D printing aficionado, you can download the trajectoid algorithm and try it out for yourself.)
Trajectoids are more than just a fancy party trick, or a devious way to annoy your Dungeon Master. Such objects could help robots travel along set trajectories, as engineers could mathematically guarantee a set path for these robots. These strange, asymmetrical shapes can also be leveraged to investigate the infinitesimally small—the quantum dynamics of qubits.
“Our study is motivated largely by fundamental curiosity,” Sobolev and his colleagues write in the paper, “but the existence of trajectoids for most paths has unexpected implications for quantum and classical optics, as the dynamics of qubits, spins and light polarization can be exactly mapped to trajectoids and their paths.”
These aren’t the first atypically shaped objects that’ve become a fascination with mathematicians. For example, the oloid—which sort of looks like a sci-fi spaceship—was designed back in 1929. Unlike most shapes, every point on the surface of the oloid touches the plane on which its rolling, giving the strange shape an almost axial rotation. Today, this mathematically perfected shape has a variety of industrial applications.
Who knows if Sabolev’s creations will have similar uses, but for tabletop RPG players, trajectoids could be a critical hit.
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