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