Arc (geometry)

From Wikipedia, the free encyclopedia

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 a circle. If the arc segment occupies a great circle (or great ellipse), it is considered a great-arc segment.

The length of a circular arc of a circle with radius r and subtending an angle θ (measured in radians) with the circle center, equals θr. This is because the following ratio holds true:

Substituting in the circumference

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

L = θr

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

and so the arc length equals then

[edit] See also

• Arc length
• Other meanings of arc

[edit] 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.