Kreisform

Kreisform is the term used in German to describe the circular form of a figure, whose defining characteristic is that all points lie at the same distance from a fixed center. In mathematical usage it corresponds to what in English is called a circle. The phrase emphasizes the round, symmetrical nature of the shape, typically in a planar context.

Key properties of a Kreisform include its center and radius. The radius r is the distance from the center to any point on the circle, the diameter d equals 2r, the circumference C equals 2πr, and the area A equals πr^2. A circle is highly symmetric, possessing infinite lines of symmetry and continuous rotational symmetry around its center.

In coordinate geometry, a Kreisform with center at (h, k) and radius r is described by the equation (x − h)^2 + (y − k)^2 = r^2. Parametric representations include x = h + r cos t, y = k + r sin t for t in [0, 2π). The circle is the 2D boundary of a disk, and in higher dimensions its analogue is the sphere (the 3D boundary of a ball).

Variants and related concepts include the disk (the filled interior of the circle) and the circumference (the boundary itself). In practical terms, Kreisformen appear in design, engineering, architecture, coins, wheels, lenses, and many natural and manufactured objects where roundness is a key feature.

See also: circle, disk, circumference, area, geometry.