The Crooked Geometry of Round Trips — Quanta Magazine

My latest column for Quanta Magazine explores what round-the-world trips would look like if we didn’t live on a sphere.

Have you ever wondered what life would be like if Earth weren’t shaped like a sphere? We take for granted the smooth ride through the solar system and the seamless sunsets afforded by the planet’s rotational symmetry. A round Earth also makes it easy to figure out the fastest way to get from point A to point B: Just travel along the circle that goes through those two points and cuts the sphere in half. We use these shortest paths, called geodesics, to plan airplane routes and satellite orbits.

But what if we lived on a cube instead? Our world would wobble more, our horizons would be crooked, and our shortest paths would be harder to find.

Classification of geodesic paths on platonic solids didn’t happen until relatively recently, and the case of the dodecahedron offers quite a surprise! To learn more, read the full article here.