A turn is a unit of plane angle measurement equal to radians, 360 degrees or 400 gradians. Subdivisions of a turn include half-turns, quarter-turns, centiturns, milliturns, etc. The closely related terms cycle and revolution are not equivalent to a turn, since these are not units of angle. Subdivisions A turn can be divided in 100 centiturns or milliturns, with each milliturn corresponding to an angle of 0.36°, which can also be written as 21′ 36″. A protractor divided in centiturns is normally called a "percentage protractor". Binary fractions of a turn are also used. Sailors have traditionally divided a turn into 32 compass points, which implicitly have an angular separation of 1/32 turn. The binary degree, also known as the binary radian (or brad), is turn. The binary degree is used in computing so that an angle can be represented to the maximum possible precision in a single byte. Other measures of angle used in computing may be based on dividing one whole turn into equal parts for other values of . The notion of turn is commonly used for planar rotations. History The word turn originates via Latin and French from the Greek word ( – a lathe). In 1697, David Gregory used (pi over rho) to denote the perimeter of a circle (i.e., the circumference) divided by its radius. However, earlier in 1647, William Oughtred had used (delta over pi) for the ratio of the diameter to perimeter. The first use of the symbol on its own with its present meaning (of perimeter divided by diameter) was in 1706 by the Welsh mathematician William Jones. Euler adopted the symbol with that meaning in 1737, leading to its widespread use. The Latin word for turn is versor, which represents a rotation about an arbitrary axis in three-dimensional space. Versors form points in elliptic space and motivate the study of quaternions, an algebra developed by W. R. Hamilton in the 1840s. Percentage protractors have existed since 1922, but the terms centiturns, milliturns and microturns were introduced much later by the British astronomer Fred Hoyle in 1962. Some measurement devices for artillery and satellite watching carry milliturn scales. Unit symbols The German standard DIN 1315 (March 1974) proposed the unit symbol "pla" (from Latin: 'full angle') for turns. Covered in (October 2010), the so-called ('full angle') is not an SI unit. However, it is a legal unit of measurement in the