Definition:Geodesic/Informal Definition

Definition

Let $S$ be a surface.

A geodesic is an arc between two points $A$ and $B$ on $S$ which has the smallest arc length from $A$ and $B$ lying completely in $S$.

Examples

Sphere

A geodesic on the surface $S$ of a sphere between points $A$ and $B$ on $S$ is the part of the great circle on which $A$ and $B$ both lie.

Also see

• Results about geodesics can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): geodesic
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): geodesic