teilkreis

Teilkreis is a German term formed from teil (part) and Kreis (circle). In many mathematical and technical texts it denotes a portion of a circle. The most common interpretation is a connected piece of the circumference between two points on the circle, i.e., a circular arc. Depending on the context, the term may also be used more broadly to refer to the closed region bounded by that arc and the corresponding radii, which is the sector of the circle.

In precise geometric language, a circle’s arc (Bog en) is the curve itself, while the sector (Sektor) is the two radii together with the arc. Regions bounded by an arc and a chord are typically called a Kreisabschnitt or Kreissegment. Because Teilkreis is not a strictly standard term, many authors prefer the clearer terms Bogen for the arc and Sektor or Kreisabschnitt for the corresponding area.

If the central angle subtending the Teilkreis is theta (in radians) and the circle has radius r, then the arc length equals s = r * theta. The area of the associated sector is A = (1/2) * r^2 * theta. The chord length c relating to theta is c = 2 r sin(theta/2). These relations connect Teilkreis to more widely used concepts such as arcs, sectors, and circle segments.

Applications of the idea include geometric constructions, architectural designs, navigation on circular paths, and any context where a partial circle or a circular arc is analyzed.

See also: Kreis, Bogen, Sektor, Kreisabschnitt, Segment eines Kreises.