Turn (geometry)

A turn is a unit of plane angle measurement equal to 2π radians, 360 degrees or 400 gradians. A turn is also referred to as a cycle (abbreviated cyc), revolution (abbreviated rev), complete rotation (abbreviated rot) or full circle. Subdivisions of a turn include half turns, quarter turns, centiturns, milliturns, points, etc. A turn can be divided in 100 centiturns or 1000 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. The binary degree, also known as the binary radian (or brad), is 1/256 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 2n equal parts for other values of n. The notion of turn is commonly used for planar rotations. The word turn originates via Latin and French from the Greek word τόρνος (tórnos – a lathe). In 1697, David Gregory used π/ρ (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 δ/π (delta over pi) for the ratio of the diameter to perimeter. The first use of the symbol π 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. 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.