Category:Sectors

This category contains results about Sectors.
Definitions specific to this category can be found in Definitions/Sectors.

Sector of Circle

A sector of a circle is the region bounded by two radii and an arc.

In the words of Euclid:

A sector of a circle is the figure which, when an angle is constructed at the center of the circle, is contained by the straight lines containing the angle and the circumference cut off by them.

(The Elements: Book $\text{III}$: Definition $10$)

In the diagram below, $BAC$ is a sector.

Spherical Sector

A spherical sector is a surface of revolution of a sector of a circle $C$ rotated $360 \degrees$ around a diameter of $C$.

The surfaces of the spherical sector are:

the zone of $S$, formed by the arc of the sector

one or two conical surfaces formed by the radius or radii of the sector

where $S$ is the sphere formed as the surface of revolution of $C$ as it rotates $360 \degrees$ around the same diameter of $C$.