did you see the words?

-

💭🕯🌥🍂🥮🌾🍯🌾🥮🍂🌥🕯💭

to bring balance and abundance to you this september season;

Going straight ahead on a complicated surface isn’t really that straightforward.

Mathematically, the paths you get by going straight ahead are called geodesics and are modelled by geodesic equations. Although they can be solved numerically and even explicitely for certain well-behaved surfaces (such as spheres), the evolution and long-term behaviour of these geodesics is very hard to predict.

A recent Numberphile video discusses a similar problem on polyhedra. These are piecewise linear, non-smooth surfaces, but again the behaviour of “going straight ahead”—simple as it may sound—can get really complicated. There have been new results on the dodecahedron, one of the Platonic solids, polyhedra that were thought to be well understood since antiquity!