Definition:Great Circle

Definition

Let $S$ be a sphere.

A great circle of $S$ is defined as the intersection of $S$ with a plane passing through the center of $S$.

Pole of Great Circle

Let $C$ be a great circle of $S$.

Let $AB$ be the diameter of $S$ situated perpendicular to the plane of $C$.

The points $A$ and $B$, where the diameter intersects $S$, are the poles of the great circle $C$.

Axis of Great Circle

The axis of a great circle $C$ is the straight line that joins the poles of $C$.

Examples

Earth's Surface

A great circle between two locations $A$ and $B$ on the surface of Earth can be used as the shortest distance to travel from $A$ to $B$.

Also see

• Results about great circles can be found here.

Sources

• 1976: W.M. Smart: Textbook on Spherical Astronomy (6th ed.) ... (previous) ... (next): Chapter $\text I$. Spherical Trigonometry: $2$. The spherical triangle.
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): great circle: 1.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): great circle
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): great circle
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): great circle