Solid Angle

In plane geometry, that part cf a plane area lying between two lines meeting at a point (the apex) is called an angle. The size of an angle can be indicated in two different ways, viz: a)the whole plane area may be divided (by lines passing through the apex of the angle) into 360 equal parts (degrees), the angle being then expressed in degrees.b)with the apex of the angle as centre a circle of any radius may be drawn. Use is then made of the fact that the arc of the circle enclosed by the two lines forming the angle is proportional to the angle. The length of the arc, expressed in terms of the radius is employed as a measure of the angle. The unit is the angle subtended by an arc of the same length as the radius of the circle, this unit being known as the radian: 1 radian = 57°17′44.8″. A plane angle is therefore <math display='block'> <mrow> <mfrac> <mrow> <mi>a</mi><mi>r</mi><mi>c</mi><mi>&#x0020;</mi><mi>l</mi><mi>e</mi><mi>n</mi><mi>g</mi><mi>t</mi><mi>h</mi> </mrow> <mrow> <mi>r</mi><mi>a</mi><mi>d</mi><mi>i</mi><mi>u</mi><mi>s</mi> </mrow> </mfrac> </mrow> </math>$$\frac{{arc length}}{{radius}}$$ radians