Donutkappale

Donutkappale is a Finnish term used to describe a donut-shaped object, most commonly a torus in geometry. The word combines donut with kappale, meaning object or piece. In mathematics and physics, the donut shape is studied for its distinctive geometry, topology, and applications.

Geometrically, a torus is the surface of revolution obtained by rotating a circle of radius r around an axis in the same plane that does not intersect the circle. When the body is hollow, the resulting shape is a toroidal surface; when the solid is filled, the object is a solid torus. The geometry is described by the major radius R, the distance from the center of the hole to the center of the tube, and the minor radius r, the radius of the tube itself. A common condition for a standard torus is R > r, ensuring the hole remains open and the surface does not self-intersect.

Key properties include a genus of 1 in topology, indicating a single hole. The volume of a solid torus is V = 2 π^2 R r^2, and its surface area is A = 4 π^2 R r. These formulas assume the standard torus where the circle is rotated about an external axis.

Donutkappale appears across disciplines: as a classic example in topology and geometry, in computer graphics as a common primitive, and in physics and engineering where toroidal shapes are used, for instance in magnetic confinement devices and various mechanical components. The term captures both the everyday idea of a doughnut and the precise mathematical concept of a torus.