cirkler

Cirkler is the Danish and Norwegian plural of cirkel, meaning circles. In mathematics it denotes the set of all points at a fixed distance from a given center, but the term is also used more broadly to refer to social groups or networks, such as circles of friends or professional circles.

In geometry, a circle is defined by its center and radius r. The circumference, the length around the circle, is C = 2πr. The area enclosed by the circle is A = πr^2. The diameter is d = 2r. The unit circle uses r = 1 and is described by x^2 + y^2 = 1 in Cartesian coordinates. A circle is often distinguished from a disk, where the disk includes the interior as well as the boundary.

Etymology and cognates: the term derives from Latin circulus, from Greek kyklos, and has given rise to related words in many European languages. The Danish and Norwegian forms cirkel and cirkler reflect this lineage.

Applications and usage: circles appear across mathematics, including geometry and trigonometry, as well as in engineering, architecture, design, and art. They are fundamental in topics such as circular motion, optics, and map projections. In everyday language, cirkler can describe social or professional networks, such as the inner circles of influence or collaboration.

Overall, cirkler encompasses both the precise geometric concept of a set of points at a fixed distance from a center and its broader metaphorical use to describe connected groups of people or ideas.