# Turn (angle)

**turnturnsrevolutionrevolvingTurn (geometry)TaucycleUnit angle2360°**

A turn is a unit of plane angle measurement equal to 2degrees or 400 gradians.wikipedia

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### Degree (angle)

**°degreesdegree**

A turn is a unit of plane angle measurement equal to 2degrees or 400 gradians.

A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360 degrees.

### Gradian

**gradgongrads**

A turn is a unit of plane angle measurement equal to 2degrees or 400 gradians.

It is equivalent to 1⁄400 of a turn, 9⁄10 of a degree, or undefined⁄200 of a radian.

### Angle

**acute angleobtuse angleoblique**

A turn is a unit of plane angle measurement equal to 2degrees or 400 gradians.

In some contexts, such as identifying a point on a circle or describing the orientation of an object in two dimensions relative to a reference orientation, angles that differ by an exact multiple of a full turn are effectively equivalent.

### Perimeter

**Perimeter lengthperimeter of the polygon**

In 1697, David Gregory used undefined⁄ρ (pi over rho) to denote the perimeter of a circle (i.e., the circumference) divided by its radius.

The perimeter of a wheel/circle (its circumference) describes how far it will roll in one revolution.

### Radian

**radiansradmicroradian**

A turn is a unit of plane angle measurement equal to 2degrees or 400 gradians.

Radians can be converted to turns (complete revolutions) by dividing the number of radians by 2.

### Binary scaling

**binary radianBinary Angular Measurement SystemBinary degree**

Binary fractions of a turn are also used.

In some cases, it is convenient to use unsigned multiplication (rather than signed multiplication) on a binary angle, which gives the correct angle in the range of 0 to +360° degrees (+2π radians or +1 turn).

### Angular unit

**angular measurementsangularmultiples of**

An angular mode was suggested for the WP 43S as well, but the calculator instead implements (multiples of ) as mode and unit since 2019.

In some contexts, such as identifying a point on a circle or describing the orientation of an object in two dimensions relative to a reference orientation, angles that differ by an exact multiple of a full turn are effectively equivalent.

### Revolutions per minute

**rpmr.p.m.RPMs**

Revolutions per minute (abbreviated rpm, RPM, rev/min, r/min, or with the notation min −1 ) is the number of turns in one minute.

### Pi

**ππ\pi**

A turn is a unit of plane angle measurement equal to 2degrees or 400 gradians.

In 1958 Albert Eagle proposed replacing by τ (tau), where

### Protractor

A protractor divided in centiturns is normally called a percentage protractor.

### Percentage

**percent%FG%**

A protractor divided in centiturns is normally called a percentage protractor.

### Winding number

**turning numberindexwinds**

Then the winding number of the curve is equal to the total number of counterclockwise turns that the object makes around the origin.

### Complex number

**complexreal partimaginary part**

A turn may be represented in a mathematical model that uses expressions of complex numbers or quaternions.

corresponds to rotating the position vector counterclockwise by a quarter turn (90°) about the origin

### Rotation

**rotatingrotatespin**

The speed of rotation is given by the angular frequency (rad/s) or frequency (turns per time), or period (seconds, days, etc.).

### Tau

**ΤTGreek letter Tau**

In 2010, Michael Hartl proposed to use tau to represent Palais' circle constant:

### Dyadic transformation

**Bernoulli mapdoubling mapBit shift map**

Here, the map doubles angles measured in turns.

### External ray

**anglesexternalexternal and internal rays**

Principal value of external angles are measured in turns modulo 1

### Polar coordinate system

**polar coordinatespolarpolar coordinate**

In the complex plane every non-zero number has a polar coordinate expression z = r cis(a) = r cos(a) + ri sin(a) where r > 0 and a is in [0, 2).

Adding any number of full turns (360°) to the angular coordinate does not change the corresponding direction.

### Kinematics

**kinematickinematicalkinetic**

In kinematics, a turn is a rotation less than a full revolution.

Common descriptions include Euler angles and the kinematics of turns induced by algebraic products.

### Frank Morley

**F. MorleyMorley, FrankProfessor Frank Morley**

Frank Morley consistently referred to elements of the unit circle as turns in the book Inversive Geometry, (1933) which he coauthored with his son Frank Vigor Morley.

Some non-standard terminology is used such as "base-circle" for unit circle and "turn" for a point on it.

### Angle of rotation

**angles of rotationangleangle ''θ'' of rotation**

A clockwise rotation is considered a negative rotation, so that, for instance, a rotation of 310° (counterclockwise) can also be called a rotation of –50° (since 310° + 50° = 360°, a full rotation (turn)).

### Unit circle

**circleBase circle (mathematics)base-circle**

A turn of the complex plane arises from multiplying z = x + iy by an element u = exp(b i) that lies on the unit circle:

### Versor

**unit quaternionhyperbolic versorhyperbolic versors**

The Latin term for turn is versor, which is a quaternion that can be visualized as an arc of a great circle.

### Spat (unit)

**spat**

* Turn (geometry) — the 2D counterpart of the spat, equivalent to 2 radians

### Unit interval

**closed unit interval[0,1interval**