# Turn (geometry)

(Redirected from Cycle)

A turn is a unit of plane angle, equal to 360° or 2π radians. As an angular unit it is mainly useful for large angles, such as in connection with coils and rotating objects. See also winding number.

A turn is also named as revolution or complete rotation or cycle.

The British astronomer and science writer Sir Fred Hoyle (1915 - 2001) in Astronomy (London 1962), proposed dividing the circle, or turn into 1000 milliturns, with each milliturn corresponding to an angle of 21' 36", or 0.36 degrees.

## Examples of use

Turn is used in complex dynamics for measure of external and internal angles

### Conversion of some common angles

Units Values
Revolutions   0 1/12 1/8 1/6 1/4 1/2 3/4 1
Degrees   30° 45° 60° 90° 180° 270° 360°
Radians 0 $\frac{\pi}{6}$ $\frac{\pi}{4}$ $\frac{\pi}{3}$ $\frac{\pi}{2}$ $\pi\,$ $\frac{3\pi}{2}$ $2\pi\,$
Grads 0g 33⅓g 50g 66⅔g 100g 200g 300g 400g