Arc (geometry)

From Wikipedia, the free encyclopedia

In Euclidean geometry, a circular arc is a closed segment of a differentiable curve in the two-dimensional plane; for example, an 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 an arc of a circle with radius <math>r</math> and subtending an angle <math>\theta\,\!</math> (measured in radians) with the circle center—i.e., the central angle—equals <math>\theta r\,\!</math>. This is because

<math>\frac{L}{\mathrm{circumference}}=\frac{\theta}{2\pi}.\,\!</math>

Substituting in the circumference

<math>\frac{L}{2\pi r}=\frac{\theta}{2\pi},\,\!</math>

and solving for arc length, <math>L</math>, in terms of <math>\theta\,\!</math> yields

<math>L=\theta r.\,\!</math>

For an angle <math>\alpha</math> measured in degrees, the size in radians is given by

<math>\theta=\frac{\alpha}{180}\pi,\,\!</math>

and so the arc length equals then

<math>L=\frac{\alpha\pi r}{180}.\,\!</math>

[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.

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