Great Circle Route
In geometry, a “great circle” is a flat plane that cuts through the middle of a sphere. Essentially, it becomes the longer line that was be drawn around that sphere.
In aviation navigation, a “great circle route” is the shortest path between two points, and is achieved by finding the great circle that both points are on. This is invariably an arc, not a straight line.
Indeed, “straight” doesn’t mean much when talking about a sphere, because the entire surface is curved – nothing on a sphere is “straight.” When looking on a sphere, the great circle route actually looks fairly straight. It only appears to be a curved line or arc when flatten to a Mercator projection map. (See image on this page.)
The great circle routes are why flights between the U.S. and Europe arc up and over the arctic circle, rather that going directly east or west.
Why I Looked It Up
Great circle routes were a plot point in REAMDE. Terrorists had access to a private jet in Xiamen, China, and were trying to figure out how to get it into North America. From Xiamen, they can’t fly a great circle route to Toronto, because it takes them over China, North Korea, and Siberia. What they can do is plot a great circle route to Calgary, which takes them just off the coast of Asia. They ended up somewhere north of Idaho after having gone over the north pole.
Also, I remember flying from Paris to Los Angeles once. On the in-flight map, I saw that we entered the United States in northern Montana, coming south over Canada.