Caption: A map illustrating the jetstream and the great circle airway between San Francisco and Tokyo.

A great-circle distance is the global minimum distance between any 2 on a sphere (i.e., an ordinary sphere or a 2-sphere) if it subtends ≤ 180° (as seen from the sphere center). If it subtends > 180°, it is a local minimum distance: i.e., it is minimum distance compared to a path with just small deviations from the great circle path.

A great circle is a circle that cuts a sphere in half. A small circle is a circle that cuts a sphere into unequal parts.

Airways often follow great circles to save fuel and travel time. This is why flights to Tokyo are often over the Aleutian Islands and flights to Europe are often over Greenland even though these flights look like the long ways on a Mercator projection map. They look short on globes. The use of great circles in traveling is called great-circle navigation.

A great circle
is an example of
a geodesic: the
stationary path
between points
in spaces with general curvature.
A stationary path is
one where infinitesimal variations from cause **NO** change in length.
Minimum
and maximum paths
(global or local)
are stationary paths.
Stationary paths
are analyzed in
variational calculus.

Credit/Permission: User:ChaosNil,
2007 /
Public domain.

Image link: Wikipedia:
File:Greatcircle Jetstream routes.svg.

Local file: local link: great_circle_path.html.

File: Mathematics file:
great_circle_path.html.