1
"Geometry Dash" Turn Down For What-By: Pluto (me)
"Geometry Dash" Turn Down For What-By: Pluto (me)
DATE: 2015/03/07::
2
TURN DOWN FOR WHAT!!??!! - Geometry Dash Part 1
TURN DOWN FOR WHAT!!??!! - Geometry Dash Part 1
DATE: 2015/03/15::
3
Geometry Dash Don´t Move | TURN DOWN FOR WHAT! | Axel 031
Geometry Dash Don´t Move | TURN DOWN FOR WHAT! | Axel 031
DATE: 2015/04/17::
4
Geometry dash - turn down for what
Geometry dash - turn down for what
DATE: 2015/05/04::
5
Moving Into Geometry Flips Slides and Turns
Moving Into Geometry Flips Slides and Turns
DATE: 2009/08/31::
6
Geometry Dash 2 Nivel Completo Turn Down For What
Geometry Dash 2 Nivel Completo Turn Down For What
DATE: 2015/02/03::
7
Colin Dodds - Geometric Transformations (Math Song)
Colin Dodds - Geometric Transformations (Math Song)
DATE: 2013/10/21::
8
Houdini 10 Tutorial - How To Turn Particles Into Geometry
Houdini 10 Tutorial - How To Turn Particles Into Geometry
DATE: 2010/06/26::
9
Top 5 hidden shortcuts and Easter eggs on geometry dash (TURN VOLUME UP)
Top 5 hidden shortcuts and Easter eggs on geometry dash (TURN VOLUME UP)
DATE: 2015/01/27::
10
"Geometry Dash" TURN DOWN FOR WHAT By: Pluto (me)
"Geometry Dash" TURN DOWN FOR WHAT By: Pluto (me)
DATE: 2015/03/05::
11
Modular Environments - Part 4 - Turning Textures into Geometry Part 2
Modular Environments - Part 4 - Turning Textures into Geometry Part 2
DATE: 2015/04/08::
12
Geometry Dash Nivel - Turn Down For Want
Geometry Dash Nivel - Turn Down For Want
DATE: 2015/04/23::
13
Geometry Dash - Creator Contest For 50 Subs! (Turn on Annotations) Over now
Geometry Dash - Creator Contest For 50 Subs! (Turn on Annotations) Over now
DATE: 2015/03/13::
14
What
What's New in SolidCAM 2010: Solid Turn Geometry Selection
DATE: 2010/03/12::
15
GEOMETRY DASH LEVEL 6 COMPLETE %100 +Turn Down For What #3
GEOMETRY DASH LEVEL 6 COMPLETE %100 +Turn Down For What #3
DATE: 2015/04/29::
16
Accidentally found a secret turn down for what (geometry dash) ( ͡° ͜ʖ ͡°)
Accidentally found a secret turn down for what (geometry dash) ( ͡° ͜ʖ ͡°)
DATE: 2015/05/04::
17
Turn Down For What Geometry Dash
Turn Down For What Geometry Dash
DATE: 2015/04/29::
18
Geometry Dash : Gameplay Part 2 Level 3 - Polargeist (Caden
Geometry Dash : Gameplay Part 2 Level 3 - Polargeist (Caden's Turn)
DATE: 2015/01/09::
19
Skateboard truck turn geometry
Skateboard truck turn geometry
DATE: 2015/04/23::
20
geometry dash turn down for wath
geometry dash turn down for wath
DATE: 2015/03/30::
21
Geometry: Slide,Flip and Turn
Geometry: Slide,Flip and Turn
DATE: 2015/04/08::
22
GEOMETRY DASH-NIVEL TURN DOWN FOR WHATᴴᴰ
GEOMETRY DASH-NIVEL TURN DOWN FOR WHATᴴᴰ
DATE: 2015/04/18::
23
Geometry Dash #2 - Turn Down for What
Geometry Dash #2 - Turn Down for What
DATE: 2015/05/14::
24
Geometry Dash Level 1 Up and Down turn around (selfmade)
Geometry Dash Level 1 Up and Down turn around (selfmade)
DATE: 2015/05/06::
25
Geometry dash creator contest #2 turn annotations on
Geometry dash creator contest #2 turn annotations on
DATE: 2015/03/08::
26
Outside In
Outside In
DATE: 2011/04/23::
27
Geometry Dash Creator Contest! Turn annotations on
Geometry Dash Creator Contest! Turn annotations on
DATE: 2015/03/23::
28
Geometry Dash | Darude Sandstorm | [1080p HD]
Geometry Dash | Darude Sandstorm | [1080p HD]
DATE: 2014/10/18::
29
Modular Environments - Part 3 - Turning Textures into Geometry
Modular Environments - Part 3 - Turning Textures into Geometry
DATE: 2015/04/06::
30
QUE MUSICA!!/TURN DOWN FOR FIRST,BY REIZOR999 (YO)/GEOMETRY DASH
QUE MUSICA!!/TURN DOWN FOR FIRST,BY REIZOR999 (YO)/GEOMETRY DASH
DATE: 2015/04/30::
31
Geometry Dash - Turn Down For What
Geometry Dash - Turn Down For What
DATE: 2015/02/28::
32
Geometry - measuring circles, flip slide turn, axis of symmetry
Geometry - measuring circles, flip slide turn, axis of symmetry
DATE: 2014/04/07::
33
Geometry Dash : Gameplay Part 2 Level 3 - Polargeist (Caden
Geometry Dash : Gameplay Part 2 Level 3 - Polargeist (Caden's Turn)
DATE: 2015/03/12::
34
Geometry Dash y el TURN DOWN FOR WHAT
Geometry Dash y el TURN DOWN FOR WHAT
DATE: 2015/02/09::
35
Johnny the Guinea Pig Teaches Geometry
Johnny the Guinea Pig Teaches Geometry
DATE: 2008/02/08::
36
Geometry Dash Turn Easy :D
Geometry Dash Turn Easy :D
DATE: 2015/05/10::
37
Denise Carter
Denise Carter's Smarty Bunch - GEOMETRY TRANSFORMATIONS
DATE: 2010/09/09::
38
i forget to turn on my mic... | Geometry Dash [PC]
i forget to turn on my mic... | Geometry Dash [PC]
DATE: 2015/05/14::
39
Geometry Wars Retro Evolved (turn down your speakers)
Geometry Wars Retro Evolved (turn down your speakers)
DATE: 2014/10/03::
40
Geometry dash Turn Down For What
Geometry dash Turn Down For What
DATE: 2015/05/04::
41
Geometry Dash - Best Auto level EVER?! - Absolute Zero by Fearotic
Geometry Dash - Best Auto level EVER?! - Absolute Zero by Fearotic
DATE: 2015/01/10::
42
How to Turn a Sphere Inside Out
How to Turn a Sphere Inside Out
DATE: 2007/11/15::
43
Applying Sacred Geometry to Music
Applying Sacred Geometry to Music
DATE: 2014/02/10::
44
SOLIDWORKS - How To Create Reference Geometry Axis
SOLIDWORKS - How To Create Reference Geometry Axis
DATE: 2015/03/20::
45
Geometry Dash 100 likes icon glitch!----[NOT WORK ON 1.93]
Geometry Dash 100 likes icon glitch!----[NOT WORK ON 1.93]
DATE: 2014/11/26::
46
The Geometry of Golf
The Geometry of Golf
DATE: 2011/03/21::
47
Geometry Dash - Fallen Rainbows 3 (preview 3) - ZeuzK (me) and XStar7 [Now it
Geometry Dash - Fallen Rainbows 3 (preview 3) - ZeuzK (me) and XStar7 [Now it's your turn XStar]
DATE: 2015/04/12::
48
Geometry MierDash
Geometry MierDash
DATE: 2015/05/17::
49
Geometry Dash - Hyperzone - Mypart
Geometry Dash - Hyperzone - Mypart
DATE: 2015/05/06::
50
Geometry Dash - Aqua Bolt by DWShin
Geometry Dash - Aqua Bolt by DWShin
DATE: 2015/01/28::
NEXT >>
RESULTS [51 .. 101]
From Wikipedia, the free encyclopedia
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Counterclockwise rotations about the center point where a complete rotation is equal to 1 turn

A turn is a unit of angle measurement equal to 360° or 2π radians. A turn is also referred to as a revolution or complete rotation or full circle or cycle or rev or rot.

A turn can be subdivided in many different ways: into half turns, quarter turns, centiturns, milliturns, binary angles, points etc.

Subdivision of turns[edit]

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.[1] The binary degree is used in computing so that an angle can be efficiently represented in a single byte (albeit to limited precision). Other measures of angle used in computing may be based on dividing one whole turn into 2n equal parts for other values of n.[2]

The notion of turn is commonly used for planar rotations. Two special rotations have acquired appellations of their own: a rotation through 180° is commonly referred to as a half-turn (\pi radians),[3] a rotation through 90° is referred to as a quarter-turn. A half-turn is often referred to as a reflection in a point since these are identical for transformations in two-dimensions.

History[edit]

The word turn originates via Latin and French from the Greek word τόρνος (tornos – a lathe).

In 1697, David Gregory used \pi/\rho (pi/rho) to denote the perimeter of a circle (i.e., the circumference) divided by its radius.[4][5] However, earlier in 1647, William Oughtred had used \delta/\pi (delta/pi) for the ratio of the diameter to perimeter. The first use of the symbol \pi on its own with its present meaning (of perimeter divided by diameter) was in 1706 by the Welsh mathematician William Jones.[6] Euler adopted the symbol with that meaning in 1737, leading to its widespread use.

Percentage protractors have existed since 1922,[7] but the terms centiturns and milliturns were introduced much later by Sir Fred Hoyle.[8]

Mathematical constants[edit]

One turn is equal to (≈6.283185307179586)[9] radians.

The circumference of the unit circle (whose radius is one) is 2π.

Conversion of some common angles[edit]

Units Values
Turns   0 1/24 1/12 1/10 1/8 1/6 1/5 1/4 1/3 2/5 1/2 3/4 1
Radians 0 π/12 π/6 π/5 π/4 π/3 2π/5 π/2 2π/3 4π/5 π 3π/2 2π
Degrees   15° 30° 36° 45° 60° 72° 90° 120° 144° 180° 270° 360°
Grads 0g 16 2/3g 33 1/3g 40g 50g 66 2/3g 80g 100g 133 1/3g 160g 200g 300g 400g

Tau proposal[edit]

An arc of a circle with the same length as the radius of that circle corresponds to an angle of 1 radian. A full circle corresponds to a full turn, or approximately 6.28 radians, which are expressed here using the Greek letter tau (τ).

In 2001, Robert Palais proposed using the number of radians in a turn as the fundamental circle constant instead of \pi, which amounts to the number of radians in half a turn, in order to make mathematics simpler and more intuitive, using a "pi with three legs" symbol to denote the constant (\pi\!\;\!\!\!\pi = 2 \pi).[10] In 2010, Michael Hartl proposed to use the Greek letter τ (tau) instead for two reasons. First, τ is the radian angle measure for one turn of a circle, which allows fractions of a turn to be expressed, such as \tfrac{2}{5}\tau for a \tfrac{2}{5} turn or \tfrac{4}{5} \pi. Second, τ visually resembles π, whose association with the circle constant is unavoidable.[11] Hartl's Tau Manifesto gives many examples of formulas that are simpler if tau is used instead of pi.[12][13][14]

Examples of use[edit]

  • As an angular unit, the turn or revolution is particularly useful for large angles, such as in connection with electromagnetic coils and rotating objects. See also winding number.
  • The angular speed of rotating machinery, such as automobile engines, is commonly measured in revolutions per minute or RPM.
  • Turn is used in complex dynamics for measure of external and internal angles. The sum of external angles of a polygon equals one turn. Angle doubling map is used.
  • Pie charts illustrate proportions of a whole as fractions of a turn. Each one percent is shown as an angle of one centiturn.

Kinematics of turns[edit]

In kinematics a turn is a rotation less than a full revolution. A turn may be represented in a mathematical model that uses expressions of complex numbers or quaternions. In the complex plane every non-zero number has a polar coordinate expression z = r cos a + r i sin a where r > 0 and a is in [0, 2π). A turn of the complex plane arises from multiplying z = x + iy by an element u = ebi that lies on the unit circle:

z \mapsto u z .

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

The Latin term for turn is versor, which is a quaternion that can be visualized as an arc of a great circle. The product of two versors can be compared to a spherical triangle where two sides add to the third. For the kinematics of rotation in three dimensions, see quaternions and spatial rotation.

See also[edit]

Notes and references[edit]

  1. ^ ooPIC Programmer's Guide www.oopic.com
  2. ^ Angles, integers, and modulo arithmetic Shawn Hargreaves blogs.msdn.com
  3. ^ Half Turn, Reflection in Point cut-the-knot.org
  4. ^ Beckmann, P., A History of Pi. Barnes & Noble Publishing, 1989.
  5. ^ Schwartzman, S., The Words of Mathematics. The Mathematical Association of America,1994. Page 165
  6. ^ Pi through the ages
  7. ^ Croxton, F. E. (1922), A Percentage Protractor Journal of the American Statistical Association, Vol. 18, pp. 108-109
  8. ^ Hoyle, F., Astronomy. London, 1962
  9. ^ Sequence OEISA019692.
  10. ^ Palais, R. 2001: Pi is Wrong, The Mathematical Intelligencer. Springer-Verlag New York. Volume 23, Number 3, pp. 7–8
  11. ^ Michael Hartl (March 14, 2013). "The Tau Manifesto". Retrieved September 14, 2013. 
  12. ^ Aron, Jacob (8 January 2011), "Interview: Michael Hartl: It's time to kill off pi", New Scientist 209 (2794), Bibcode:2011NewSc.209...23A, doi:10.1016/S0262-4079(11)60036-5 
  13. ^ Landau, Elizabeth (14 March 2011), "On Pi Day, is 'pi' under attack?", cnn.com 
  14. ^ "Why Tau Trumps Pi". Scientific American. 2014-06-25. Retrieved 2015-03-20. 

External links[edit]

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