Kells, Lyman M. Formerly, U.S. Naval Academy.
- Additional Readings
A radian is the angle subtended at the center of a circle by an arc of the circle equal in length to its radius. It is proved in geometry that equal central angles of two circles subtend arcs proportional to their radii; and the converse is true. Hence the radian is independent of the length of the radius. The illustration represents two circles of radius r. Arc AB of length r subtends 1 radian (rad) at the center O of the circle, and arc A′B′ of length s subtends θ rad at its center. Since arcs on equal circles are proportional to their subtended central angles, = , or formula (1)
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