Ympyräkehäseen

Ympyräkehäseen is a term used in Finnish geometry to denote the annulus, the ring-shaped region in the plane that lies between two concentric circles. The concept is defined by two radii, r1 and r2, where 0 ≤ r1 < r2. The inner boundary is the circle of radius r1 and the outer boundary is the circle of radius r2. The area of an annulus is given by A = π(r2^2 − r1^2). The region is connected but not simply connected when r1 > 0.

If r1 = 0, the ympyräkehäseen reduces to a disk. The annulus has rotational symmetry about the common center of its bounding circles, and it is naturally described in polar coordinates, which simplify many calculations over the region. In mathematics, annuli are commonly used in topics such as integrals, potential theory, and complex analysis, where they serve as domains for analytic functions.

Applications of the concept extend beyond pure mathematics. In engineering and manufacturing, annular shapes such as washers, seals, and bearings are practical realizations of ympyräkehäseen. In computer graphics and geographic information systems, annular regions model hollow circular features and buffer zones around circular objects.

Etymologically, the name combines ympyrä (circle) and kehän (ring) with a locative suffix, reflecting Finnish naming conventions for regions defined by circular boundaries. See also disk, circle, annulus, and polar coordinates for related concepts.