A circular sector is shaded in green with length L along the circle's perimeter

In Euclidean 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. A circular sector or circle sector, is the portion of a Circle enclosed by two radii and an arc. Euclidean geometry is a mathematical system attributed to the Greek Mathematician Euclid of Alexandria. In Topology and related branches of Mathematics, a closed set is a set whose complement is open. In Calculus, a branch of mathematics the derivative is a measurement of how a function changes when the values of its inputs change In Mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object The circumference is the distance around a closed Curve. Circumference is a kind of Perimeter. If the arc segment occupies a great circle (or great ellipse), it is considered a great-arc segment. A great circle is a Circle on the surface of a Sphere that has the same circumference as the sphere dividing the sphere into two equal Hemispheres. A great ellipse is an Ellipse passing through two points on a Spheroid and having the same center as that of the spheroid

The length of an arc of a circle with radius r and subtending an angle (measured in radians) with the circle center—i. Determining the length of an irregular arc segment — also called Rectification of a Curve — was historically difficult The radian is a unit of plane Angle, equal to 180/ π degrees, or about 57 e. , the central angle—equals . central angle is an Angle whose Line is the center of a Circle, and whose sides pass through a pair of points on the circle thereby Subtending This is because

Substituting in the circumference

and solving for arc length, L, in terms of yields

For an angle α measured in degrees, the size in radians is given by

and so the arc length equals then

See also

• Arc length
• Other meanings of arc
• Circular-arc graph

External links

• Definition and properties of a circular arc With interactive animation
• A collection of pages defining arcs and their properties, with animated applets Arcs, arc central angle, arc peripheral angle, central angle theorem and others. Determining the length of an irregular arc segment — also called Rectification of a Curve — was historically difficult In Graph theory, a circular-arc graph is the Intersection graph of a set of arcs on the circle
• Eric W. Weisstein, Arc at MathWorld. Eric W Weisstein (born March 18, 1969, in Bloomington Indiana) is an Encyclopedist who created and maintains MathWorld MathWorld is an online Mathematics reference work created and largely written by Eric W