“The shortest distance between two points is always a straight line in Euclidean geometry”.
This is the geometry that is usually learned in school, where the figures are two-dimensional and represented on a flat surface like a notebook sheet.
In real life, the shortest distance is a curve called geodesic. That’s because our planet is not flat! Thus, Euclidean geometry is not used, but Riemanian geometry.
This is the concept that flight planners use to chart airplane routes in order to save time and fuel. From a practical point of view, in most cases, geodesic is the shortest curve that joins two points.
This effect has interesting implications; for example, when you fly on an airplane, the path it takes to go from one destination to another does not follow a “straight line”, as many people imagine. It follows the “curvature” of the Earth, making small adjustments in the direction of travel, in order to cover the shortest possible stretch. If the plane were simply “in a straight line”, it would end up traveling a longer trajectory than it does when following the land curvature.
Absolutely wonderstruck by this revelation!!