pieslice

A pie slice, informally known as a sector, is a region of a circle bounded by two radii and the arc between them. The two straight sides are the radii that meet at the circle’s center, and the curved boundary is the arc of the circle. The term pie slice is common in everyday language and in pie charts, where slices represent portions of a whole.

Key properties include the radius r of the circle and the central angle theta that subtends the slice, measured at the circle’s center. The area of a pie slice with angle theta (in radians) is A = (1/2) r^2 theta. If theta is given in degrees, A = (theta/360) · π r^2. The fraction of the circle represented by the slice is theta/(2π) in radians or theta/360 in degrees. The length of the arc forming the curved boundary is r · theta when theta is in radians.

A related shape is the circular segment, which is the region bounded by a chord and an arc and does not necessarily include the circle’s center. The pie slice is the sector that does include the center of the circle.

Applications of pie slices include geometry problems, design contexts, and the representation of data in pie charts, where the central angle or arc length corresponds to the proportion of the whole. While “sector” is the standard mathematical term, “pie slice” remains common in colloquial use.