spherical angle

Definition

Noun:
- A geometric angle formed on the surface of a sphere: A "spherical angle" is the angle formed at the point where two arcs of great circles intersect. It is measured by the angle between the tangents to the arcs at their point of intersection or by the dihedral angle of the planes containing the great circles.

Usage

The term "spherical angle" is used in spherical geometry, astronomy, and navigation to describe angles on the surface of a sphere, such as the Earth or a celestial sphere.
It is a specific geometric concept distinct from a plane angle.

Examples

Noun:
- The spherical angle between the Greenwich meridian and the equator is 90 degrees.
- To solve the problem, we first calculated the spherical angle at vertex A of the spherical triangle.

Advanced Usage

Spherical trigonometry: The branch of geometry that deals with the relationships between spherical angles and the sides (which are arcs of great circles) of spherical triangles.
- Spherical trigonometry is essential for calculating distances and bearings in long-range navigation.

Variants and Related Words

Spherical triangle (n): A triangle on the surface of a sphere, formed by the intersections of three great circles. Its sides are arcs, and its angles are spherical angles.
Great circle (n): A circle on the surface of a sphere whose center is the center of the sphere. The shortest path between two points on a sphere lies along a great circle.
Dihedral angle (n): The angle between two intersecting planes. The measure of a spherical angle is equal to the dihedral angle between the planes of its great circles.

Synonyms

There are no direct common synonyms for this precise geometric term. Descriptive phrases include "angle on a sphere" or "angle formed by great circles."

Related Phrases

Solid angle: A related but distinct concept; a three-dimensional angle that measures how large an object appears from a point, measured in steradians. A spherical angle is a two-dimensional angle on a spherical surface.

Noun