Why are airplane routes curved and not straight?

Airplane flights do not follow a straight line but rather a curved path, and this choice goes beyond any technical issue—it is an adaptation to the curvature of the planet itself. In geometry, we learn that the shortest distance between two points is a straight line, but this principle applies only to flat surfaces, like a sheet of paper. When considering the spherical shape of the Earth, the shortest distance between two points becomes a curve known as a geodesic.

This concept originates from Riemannian geometry, which is better suited to curved surfaces. Flight planners use this approach to map out the shortest routes to save time and fuel. These geodesic paths represent the most efficient routes on a sphere. Instead of flying in a "straight line" as it appears on a flat map, airplanes follow a curved trajectory that is, in three-dimensional reality, the shortest path.

These air routes are a fascinating testament to the Earth's curvature. Every flight follows a course that might seem counterintuitive, but in fact, represents the shortest distance and least effort on our spherical planet.

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