Definition:Spherical Angle

Definition

Let $S$ be a sphere.

Let $PQ$ be a diameter of $S$.

Let $PAQ$ and $PBQ$ be great circles on $S$ both passing through the points $P$ and $Q$.

Let tangents $S$ and $T$ to $PAQ$ and $PBQ$ respectively be drawn through $P$.

Then the angle between $S$ and $T$ is known as the spherical angle between $PAQ$ and $PBQ$.

Thus a spherical angle is defined with respect only to $2$ great circles.

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): spherical angle
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): spherical angle
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): spherical angle