TeXipedia

sphericalangle

Denotes a spherical angle in geometric and mathematical contexts, particularly in three-dimensional geometry and spherical trigonometry.

Overview

Essential in spherical geometry and mathematical astronomy where angles on curved surfaces need representation. Common applications include:

  • Navigation and geodesy calculations involving angles on a sphere
  • Astronomical coordinate transformations
  • Spherical trigonometry problems in mathematics
  • Crystal structure analysis in chemistry and materials science

Particularly valuable when working with spherical coordinates or describing angular relationships between great circles on a sphere's surface.

Examples

Denoting a spherical angle in a geometric construction.

∢ABC=60∘\sphericalangle ABC = 60^\circ 
\sphericalangle ABC = 60^\circ

Indicating the angle between vectors in spherical coordinates.

r⃗1∢r⃗2=ϕ\vec{r}_1 \sphericalangle \vec{r}_2 = \phi 
\vec{r}_1 \sphericalangle \vec{r}_2 = \phi

Representing the angular separation between celestial objects.

Angular Distance=∢P1P2=23.5∘\text{Angular Distance} = \sphericalangle P_1P_2 = 23.5^\circ 
\text{Angular Distance} = \sphericalangle P_1P_2 = 23.5^\circ