Cirkloj

Cirkloj, in Euclidean plane geometry, are the set of all points at a fixed distance, called the radius, from a given point known as the center. The distance from the center to any point on the cirklo is r, and the locus forms a closed, perfectly symmetric curve. In some contexts the term cirklo is used to refer specifically to the boundary, while the interior is called a disk; in other usages the distinction varies by tradition.

Key properties include the circumference and the area. The circumference length is C = 2πr, and the area is A = πr^2. If the diameter d is used instead of the radius, then C = πd and A = (π/4)d^2. In Cartesian coordinates, a circle with center (h,k) and radius r is described by (x − h)^2 + (y − k)^2 = r^2.

Circles arise in many contexts, from basic geometry to engineering and art. The constant π, defined as the ratio of a circle’s circumference to its diameter, is a foundational mathematical constant. While a circle is a planar figure, the concept extends to spheres and other surfaces in higher dimensions, where circles can appear as intersections or as nonplanar curves on curved spaces.

Name origin: cirkloj is the Esperanto plural for cirklo, which derives from the Latin circulus and the Greek kyklos; the term reflects a basic geometric concept of a round shape used in Esperanto and related languages.