A Plane which passes through the center of a sphere intersects
the sphere in a great circle.
For example, circle of longitude on a globe are great circles,
but circles of latitude are not great circles (except for
circles are the largest circles which can be drawn on a sphere.
Circles of latitude, apart from the equator, are not as large.
The shortest distance between two points on a sphere is along
the great circle passing through the points.
great circle is the intersection of a sphere with a plane
going through its center. A great circle can be demonstrated
by tightly stretching a piece of sewing thread across the
surface of a globe between the start and finish points of
the intended journey. Great circles serve as the analog of
straight lines in spherical geometry.