The spherical geometry that was discussed in the previous posts actually has a surprising number of real-world applications. For example, pilots and sailors use it all the time in their jobs to find the shortest path to their destination. Remember, that Earth has a spherical form and therefore the Euclidean rules of the plane applied to the surface of the planet won’t work like that.

This means that the shortest path between Los Angeles and London on Earth’s map is not a straight line (red), but rather a curve (purple) that follows a line on the sphere that is Earth.

So, the pilots, who deal with spherical geometry on a daily bases, have to go through mathematical calculations discussed here, along with other more complex derivations, every time they want to analyze the direction or the path of their journey. A perfect career choice for people who want to do math all day long.