A line of constant rhumb (constant angle with respect to all meridians) eventually spirals around a pole:

Take two locations:

Neither the rhumb line (red) nor the geodesic (green) is a straight line (given for comparison in black), using the default equirectangular geo projection:

The rhumb line is straight in the Mercator projection, and now it is superimposed on the black line:

The geodesic is straight in an azimuthal projection centered at one of the points, and now it is superimposed on the black line:

Take a polyhedron:

Get the latitude and longitude of the vertices on a sphere:

Draw the geodesics among those vertices on a world map:

Use an azimuthal projection:

A geo disk or a geo circle is constructed using the endpoints of geodesics starting from its center:

The endpoint of a geodesic path may be computed using GeoDestination:

Check the displacement data of the path using GeoDistance and GeoDirection:

Or directly with GeoDisplacement:

Construct a geodesic path that leaves London with NE direction and goes around the Earth three times:

Computations are performed on an ellipsoidal Earth by default. Hence geodesic paths do not close:

Use a spherical model for the Earth. Then the geodesic is closed:

Or use a great ellipse, which is always closed:

Take two geo positions:

For the low eccentricity of the Earth, geodesics are close to great ellipses:

For larger eccentricities, they may differ substantially: