English

Verb

subtended

1. past of subtend

In geometry, an arc subtended by an angle is a curve whose endpoints are on the angle's two rays. The precise meaning varies with the context. For example, one may speak of the arc of a circumference subtended by an angle whose vertex is a point on the circumference. A simple theorem of plane geometry states that equal angles subtend arcs of equal length in such a situation. The converse is also true: equal arc lengths subtend equal angles.

Similarly, a solid angle subtends a surface or a solid object. A solid angle is the area on a unit sphere cut out by the envelope of the vectors defining the perimeter of the surface or object. The solid angle delimited by a circular cone of opening angle (i.e. apex angle) θ is

2 \pi \left (1 - \cos \right).

See also

• Central angle

External links

• How an object subtends an angle, Math Open Reference, With interactive applet
• Angle definition pages, Math Open Reference, with interactive applets that are also useful in a classroom setting.