Definition:Sector of Circle
Definition
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.
In fact there are two sectors, together making up the whole of the circle.
When describing a sectors by means of its three defining points (as in $BAC$ above), the convention is to report them in the following order:
- $(1):\quad$ The point on the circumference at the end of the clockwise radius
- $(2):\quad$ The point at the center of the circle
- $(3):\quad$ The point on the circumference at the end of the anticlockwise radius
Thus in the sector above, $BAC$ describes the sector indicated by $\theta$, while the sector comprising the rest of the circle is described by $CAB$.
Angle of Sector
The angle of a sector of a circle is the angle between the two radii which delimit the sector.
In the above diagram, the angle of the sector $BAC$ is $\theta$.
The conjugate angle of $\theta$ also forms a sector, denoted $CAB$ (see above).
Also see
- Results about sectors of circles can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): sector
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): sector
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): sector