The straight line that isn't the shortest

A rhumb line, a straight course on Mercator, holds one compass bearing all the way to your destination: turn the ship once and hold the wheel. It is easy to steer and, except along the equator or a meridian, never the shortest way there. In 1802 Nathaniel Bowditch published The American Practical Navigator with tables for the shorter course, one that keeps changing bearing as it goes: the great circle.

A great circle is what you get by slicing the sphere with a plane through its very centre, so its arc between any two points is the shortest path over the surface there is. It is why a flight from London to Los Angeles curves up over Canada on the in-flight map instead of running due west: that curve is the straight line, on a globe.

No flat map can draw every great circle as a straight line and keep every shape and area honest at once, which is exactly this app's recurring theme. Equal Earth bends it, Mercator can make it swing the wrong way entirely, and only the globe shows the arc for what it is: the shortest string you could stretch between two pins on a ball.