In geometry, an arc is a closed segment of a differentiable curve in the two-dimensional plane; for example, a circular arc is a segment of the circumference of a circle. If the arc is part of a great circle (or great ellipse), it is called a great arc.

The length of an arc of a circle with radius Failed to parse (Missing texvc executable; please see math/README to configure.): r

. This is because

Substituting in the circumference

and solving for arc length, Failed to parse (Missing texvc executable; please see math/README to configure.): L , in terms of Failed to parse (Missing texvc executable; please see math/README to configure.): \theta\,\!

An angle of Failed to parse (Missing texvc executable; please see math/README to configure.): \alpha

and so the arc length equals

A practical way to determine the length of an arc in a circle is to plot two lines from the arc's endpoints to the center of the circle, measure the angle where the two lines meet the center, then solve for L by cross-multiplying the statement:

Arc may refer to:

Geometry (Ancient Greek: γεωμετρία; geo- "earth", -metria "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with elements of a formal mathematical science emerging in the West as early as Thales (6th Century BC). By the 3rd century BC geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow.Archimedes developed ingenious techniques for calculating areas and volumes, in many ways anticipating modern integral calculus. The field of astronomy, especially mapping the positions of the stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems during the next one and a half millennia. Both geometry and astronomy were considered in the classical world to be part of the Quadrivium, a subset of the seven liberal arts considered essential for a free citizen to master.