Gradian
<templatestyles src="Module:Hatnote/styles.css"></templatestyles>
<templatestyles src="Module:Hatnote/styles.css"></templatestyles>
| Gon | |
|---|---|
| Unit of | Angle |
| Symbol | g or gon |
| Unit conversions | |
| 1 g in ... | ... is equal to ... |
| turns | <templatestyles src="Sfrac/styles.css" />1/400 |
| radians | <templatestyles src="Sfrac/styles.css" />π/200 |
| degrees | <templatestyles src="Sfrac/styles.css" />9/10° |
The gradian is a unit of measurement of an angle, equivalent to 1⁄400 of a turn,[1] 9⁄10 of a degree or π⁄200 of a radian.
It is also known as gon (from Greek γωνία/gōnía for angle), grad, or grade. In continental Europe, the French term centigrade was in use for one hundredth of a grad. This was one reason for the adoption of the term Celsius to replace centigrade as the name of the temperature scale.[2][3]
Contents
History
The unit originated in France as the grade, along with the metric system, hence it is occasionally referred to a "metric degree". Due to confusion with existing grad(e) units of northern Europe, the name gon was later adopted, first in those regions, later as the international standard. In German, the unit was formerly also called Neugrad (new degree), likewise Nygrad in Swedish, Danish and Norwegian (also Gradian), and Nýgráða in Icelandic.
Although attempts at a general introduction were made, the unit was only adopted in some countries and for specialised areas such as surveying, mining and geology. The French artillery has used the grad for decades. The degree, 1⁄360 of a circle, or the mathematically more convenient radian, 1⁄(2π) of a circle (used in the SI system of units) are generally used instead.
In the 1970s and 1980s most scientific calculators offered the grad as well as radians and degrees for their trigonometric functions.[4] In the 2010s some scientific calculators lack support for gradians.[5]
The international standard symbol for this unit today is "gon" (see ISO 31-1). Other symbols used in the past include "gr", "grd", and "g", the last sometimes written as a superscript, similarly to a degree sign: 50g = 45°. "Grad" was commonly used on calculators with LCD displays, as "DEG", "GRAD", and "RAD" could all be represented as a subsection of a three-segment panel forming the string of letters "DEGRAD".
Benefits
Each quadrant is assigned a range of 100 gon, which eases recognition of the four quadrants, as well as arithmetic involving perpendicular or opposite angles.
| 0° | = | 0 gradians |
| 90° | = | 100 grad |
| 180° | = | 200 grade |
| 270° | = | 300 gon |
| 360° | = | 400 gradians |
One advantage of this unit is that right angles to a given angle are easily determined. If one is sighting down a compass course of 117 grad, the direction to one's left is 17 grad, to one's right 217 grad and behind one 317 grad. A disadvantage is that the common angles of 30° and 60° in geometry must be expressed in fractions (331⁄3 grad and 662⁄3 grade, respectively). Similarly, in one hour (1⁄24 day), Earth rotates by 15° or 162⁄3 gon.
Originally, 1 gradians of arc along the Earth's surface was equal to 100 kilometers of distance at the equator; therefore 1 centigrad of arc equals 1 kilometer.[6]
Gradians are also convenient when working with vectors on the complex plane. The exponent of the imaginary unit on any given vector is equal to its angle (argument) in hectogradians (100 grad) from the positive x-axis: 
has an argument of 
grade.
Use in surveying
In surveying, the gradian is the default unit of angles in many parts of the world.[7] Subdivisions of gradian used in surveying can be referred to as c and cc (1 c = 0.01 grad; 1 cc = 0.0001 grad).
Conversion
| Turns | Radians | Degrees | Gradians (Gons) |
|---|---|---|---|
| 0 | 0 | 0° | 0g |
| <templatestyles src="Sfrac/styles.css" />1/24 | <templatestyles src="Sfrac/styles.css" />π/12 | 15° | <templatestyles src="Sfrac/styles.css" />16+2/3g |
| <templatestyles src="Sfrac/styles.css" />1/12 | <templatestyles src="Sfrac/styles.css" />π/6 | 30° | <templatestyles src="Sfrac/styles.css" />33+1/3g |
| <templatestyles src="Sfrac/styles.css" />1/10 | <templatestyles src="Sfrac/styles.css" />π/5 | 36° | 40g |
| <templatestyles src="Sfrac/styles.css" />1/8 | <templatestyles src="Sfrac/styles.css" />π/4 | 45° | 50g |
| <templatestyles src="Sfrac/styles.css" />1/2π | 1 | c. 57.3° | c. 63.7g |
| <templatestyles src="Sfrac/styles.css" />1/6 | <templatestyles src="Sfrac/styles.css" />π/3 | 60° | <templatestyles src="Sfrac/styles.css" />66+2/3g |
| <templatestyles src="Sfrac/styles.css" />1/5 | <templatestyles src="Sfrac/styles.css" />2π/5 | 72° | 80g |
| <templatestyles src="Sfrac/styles.css" />1/4 | <templatestyles src="Sfrac/styles.css" />π/2 | 90° | 100g |
| <templatestyles src="Sfrac/styles.css" />1/3 | <templatestyles src="Sfrac/styles.css" />2π/3 | 120° | <templatestyles src="Sfrac/styles.css" />133+1/3g |
| <templatestyles src="Sfrac/styles.css" />2/5 | <templatestyles src="Sfrac/styles.css" />4π/5 | 144° | 160g |
| <templatestyles src="Sfrac/styles.css" />1/2 | π | 180° | 200g |
| <templatestyles src="Sfrac/styles.css" />3/4 | <templatestyles src="Sfrac/styles.css" />3π/2 | 270° | 300g |
| 1 | 2π | 360° | 400g |
See also
- Angular frequency
- Angular mil (military measurement)
- Harmonic analysis
- Steradian (the "square radian")
- Trigonometry
- cent (music)
- centitone
- Jean-Charles de Borda
- Repeating circle
- Spread
References
- ↑ Lua error in package.lua at line 80: module 'strict' not found.
- ↑ Lua error in package.lua at line 80: module 'strict' not found.. On p. 42 Frasier argues for using grads instead of radians as a standard unit of angle, but for renaming grads to "radials" instead of renaming the temperature scale.
- ↑ Lua error in package.lua at line 80: module 'strict' not found.
- ↑ Lua error in package.lua at line 80: module 'strict' not found.
- ↑ Lua error in package.lua at line 80: module 'strict' not found.
- ↑ Cartographie – lecture de carte – Partie H Quelques exemples à retenir
- ↑ Lua error in package.lua at line 80: module 'strict' not found..
