nollapituuspiiri

Nollapituuspiiri is a term used in Finnish geometry to describe a zero-length circle. It denotes a degenerate circle whose circumference is zero. In Euclidean geometry, when the circle’s radius is zero, the circumference 2πr equals zero, and the set of points at distance zero from the center reduces to the single point at the center. Therefore, a nollapituuspiiri can be viewed as a single-point geometric object.

Nomenclature and usage: The word is formed from nolla (zero), pituus (length), and piiri (circle). It is used informally, particularly in teaching to illustrate degenerate or limiting cases of circles. It is not a standard named object in most mathematical texts, where such a case is usually described simply as a circle with radius zero or as a degenerate circle.

Properties: It has zero length and zero area; as a locus, it coincides with the center. In parametric form, x = x0 + 0·cos t, y = y0 + 0·sin t yields (x(t), y(t)) = (x0, y0) for all t, demonstrating the degeneracy.

Relation to topology: In topological terms, the “circle” of radius zero is a point, and in the limit as the radius approaches zero, the circle converges to that point.

See also: Circle, Degenerate circle, Point, Radius, Topology.

References: General geometry texts discuss degenerate cases of circles and the idea that a circle with radius zero reduces to a single point; the term nollapituuspiiri is primarily a descriptive or informal label rather than a formal standard.