This is because the universe is vast, and the total angle of triangles in spherical or hyperbolic geometry is said to be very small compared to the total angle of triangles in a plane universe.

If you draw straight lines connecting those cities to make a triangle on the surface of the globe, you will find that the interior angles of that triangle add up to more than 180 degrees.

The three angles of a plane Euclidean triangle add to two right angles or 180 degrees. A triangle on the globe has three angles whose sum exceeds two right angles.

Everyone learns the number one rule about triangles in high school: the angles of a triangle add up to 180 degrees. But did you know that sometimes they don't? Triangles are much more interesting ...

Learn about angles in triangles and quadrilaterals with this BBC Bitesize Maths article. For students between the ages of 11 and 14.