Kreisbogenes

Kreisbogenes is a term used in geometry to denote the arc of a circle contained between two distinct points on the circle’s circumference. The Kreisbogenes is defined by the circle’s radius and by the central angle subtended by the two endpoints. In essence, it is the curved portion of the circumference that connects the endpoints.

Between any two points on a circle there are, in general, two Kreisbogenes: a minor arc, which is the shorter path along the circumference, and a major arc, which is the longer path. If the endpoints are opposite ends of a diameter, the two Kreisbogenes are semicircles of equal length. The length of a Kreisbogenes depends on the radius r of the circle and the measure of the central angle θ (in radians) that subtends the endpoints, with the arc length L = rθ. If θ is given in degrees, L = πrθ/180. The chord connecting the endpoints has length c = 2r sin(θ/2).

Notationally, Kreisbogenes is often denoted by arc AB, referring to the arc between points A and B on the circle. Related concepts include the sector formed by the Kreisbogenes and the circle’s radius, whose area is (1/2)r²θ (in radians), and the relationship to the circle’s circumference 2πr.

Applications of the Kreisbogenes appear in geometry, trigonometry, computer graphics, and design, where the properties of circular arcs are used to model curves, measure lengths, and calculate areas.