One of the things that we learn at school when we study geometry is that the shortest distance between two points is always a straight line. That is true in plane geometry. But if we are talking about a sphere, that statement is not correct.
The first time I went to the United States, my curiosity led me to search for maps showing the routes that airplanes follow and the surprise was huge: airplanes do not follow straight lines!
I could not understand the reason why airlines would want to make flights longer and spend more on fuel.
Thus, I learned that representing the Earth on plain surfaces as maps entails some distortions. For instance, the Mercator projection, used by Google Maps, shows us Greenland being almost as big as Africa when in reality the latter is like 14 times bigger than the former. Likewise, in this type of projection, Alaska and Brazil seem to have a similar size, even though Brazil is five times bigger than Alaska.
Therefore, thinking automatically of a straight line that unites two airports is actually a mistake. Indeed, the shortest line on a sphere will always be the one that draws the greatest circle between two points. That circle is also known as an orthodromic line. Nonetheless, it is not always possible for airplanes to follow this pattern since there are zones that are restricted to civilian air traffic. Meteorological conditions or volcanic activity may also affect an air route.
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