| gon | |
|---|---|
.jpg) Compass graded with 400 gon | |
| General information | |
| Unit of | Angle |
| Symbol | gon, ᵍ, grad |
| Conversions | |
| 1 gonin ... | ... is equal to ... |
| turns | 1/400 turn |
| radians | π/200 rad ≈ 0.0157... rad |
| milliradians | 5π mrad ≈ 15.71... mrad |
| degrees | 0.9° |
| minutes of arc | 54′ |
Intrigonometry, thegradian – also known as thegon (from Ancient Greek γωνία (gōnía) 'angle'),grad, orgrade[1] – is aunit of measurement of anangle, defined as one-hundredth of theright angle; in other words, 100 gradians is equal to 90 degrees.[2][3][4] It is equivalent to1/400 of aturn,[5]9/10 of adegree, orπ/200 of aradian. Measuring angles in gradians (gons) is said to employ thecentesimal system of angular measurement, initiated as part ofmetrication anddecimalisation efforts.[6][7][8][a]
In continentalEurope, the French wordcentigrade, also known ascentesimal minute of arc, was in use for one hundredth of a grade; similarly, thecentesimal second of arc was defined as one hundredth of a centesimal arc-minute, analogous todecimal time and thesexagesimalminutes and seconds of arc.[12] The chance of confusion was one reason for the adoption of the termCelsius to replacecentigrade as the name of the temperature scale.[13][14]
Gradians (gons) are principally used insurveying (especially in Europe),[15][7][16] and to a lesser extent inmining[17] andgeology.[18][19]
The gon (gradian) is a legally recognised unit of measurement in theEuropean Union[20]: 9 and inSwitzerland.[21] However, this unit is not part of theInternational System of Units (SI).[22][20]: 9–10
The unit originated inFrance in connection with theFrench Revolution as thegrade, along with themetric system, hence it is occasionally referred to as ametric degree. Due to confusion with the existing termgrad(e) in some northern European countries (meaning a standard degree,1/360 of a turn), the namegon was later adopted, first in those regions, and later as the international standard.[which?] In France, it was also calledgrade nouveau. InGerman, the unit was formerly also calledNeugrad (new degree) (whereas the standard degree was referred to asAltgrad (old degree)), likewisenygrad inDanish,Swedish andNorwegian (alsogradian), andnýgráða inIcelandic.
Although attempts at a general introduction were made, the unit was only adopted in some countries, and for specialised areas such assurveying,[15][7][16]mining[17] andgeology.[18][19] Today, the degree,1/360 of aturn, or the mathematically more convenientradian,1/2π of a turn (used in theSI system of units) is generally used instead.
In the1970s –1990s, mostscientific calculators offered the gon (gradian), as well as radians and degrees, for theirtrigonometric functions.[23] In the 2010s, some scientific calculators lack support for gradians.[24]
| ◌ᵍ | |
|---|---|
Gon | |
| In Unicode | U+1D4D ᵍMODIFIER LETTER SMALL G |
| Related | |
| See also | U+00B0 °DEGREE SIGN |
The international standard symbol for this unit is "gon" (seeISO 31-1, Annex B).[needs update] 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°.Ametric prefix is sometimes used, as in "dgon", "cgon", "mgon", denoting respectively 0.1 gon, 0.01 gon, 0.001 gon.Centesimal arc-minutes and centesimal arc-seconds were also denoted with superscriptsc andcc, respectively.
| Submultiples | Multiples | ||||
|---|---|---|---|---|---|
| Value | SI symbol | Name | Value | SI symbol | Name |
| 10−1 gon | dgon | decigon | 101 gon | dagon | decagon |
| 10−2 gon | cgon | centigon | 102 gon | hgon | hectogon |
| 10−3 gon | mgon | milligon | 103 gon | kgon | kilogon |
| 10−6 gon | μgon | microgon | 106 gon | Mgon | megagon |
| 10−9 gon | ngon | nanogon | 109 gon | Ggon | gigagon |
| 10−12 gon | pgon | picogon | 1012 gon | Tgon | teragon |
| 10−15 gon | fgon | femtogon | 1015 gon | Pgon | petagon |
| 10−18 gon | agon | attogon | 1018 gon | Egon | exagon |
| 10−21 gon | zgon | zeptogon | 1021 gon | Zgon | zettagon |
| 10−24 gon | ygon | yoctogon | 1024 gon | Ygon | yottagon |
| 10−27 gon | rgon | rontogon | 1027 gon | Rgon | ronnagon |
| 10−30 gon | qgon | quectogon | 1030 gon | Qgon | quettagon |
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 gradians |
| 180° | = | 200 gradians |
| 270° | = | 300 gradians |
| 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 gon, the direction to one's left is 17 gon, to one's right 217 gon, and behind one 317 gon. A disadvantage is that the common angles of 30° and 60° in geometry must be expressed in fractions (as33+1/3 gon and66+2/3 gon respectively).
| Turns | Radians | Degrees | Gradians |
|---|---|---|---|
| 0 turn | 0 rad | 0° | 0g |
| 1/72 turn | π/36 or𝜏/72 rad | 5° | 5+5/9g |
| 1/24 turn | π/12 or𝜏/24 rad | 15° | 16+2/3g |
| 1/16 turn | π/8 or𝜏/16 rad | 22.5° | 25g |
| 1/12 turn | π/6 or𝜏/12 rad | 30° | 33+1/3g |
| 1/10 turn | π/5 or𝜏/10 rad | 36° | 40g |
| 1/8 turn | π/4 or𝜏/8 rad | 45° | 50g |
| 1/2π or 𝜏 turn | 1 rad | approx. 57.3° | approx. 63.7g |
| 1/6 turn | π/3 or𝜏/6 rad | 60° | 66+2/3g |
| 1/5 turn | 2π or 𝜏/5 rad | 72° | 80g |
| 1/4 turn | π/2 or𝜏/4 rad | 90° | 100g |
| 1/3 turn | 2π or 𝜏/3 rad | 120° | 133+1/3g |
| 2/5 turn | 4π or 2𝜏 or α/5 rad | 144° | 160g |
| 1/2 turn | π or𝜏/2 rad | 180° | 200g |
| 3/4 turn | 3π or ρ/2 or3𝜏/4 rad | 270° | 300g |
| 1 turn | 𝜏 or 2π rad | 360° | 400g |
In the 18th century, themetre was defined as the 10-millionth part of aquarter meridian.Thus, 1 gon corresponds to anarc length along the Earth's surface of approximately 100 kilometres; 1 centigon to 1 kilometre; 10 microgons to 1 metre.[25] (Themetre has been redefined with increasing precision since then.)
The gradian isnot part of theInternational System of Units (SI). The EU directive on the units of measurement[20]: 9–10 notes that the gradian "does not appear in the lists drawn up by theCGPM,CIPM orBIPM." The most recent, 9th edition of theSI Brochure does not mention the gradian at all.[22] The previous edition mentioned it only in the following footnote:[26]
The gon (or grad, where grad is an alternative name for the gon) is an alternative unit of plane angle to the degree, defined as (π/200) rad. Thus there are 100 gon in a right angle. The potential value of the gon in navigation is that because the distance from the pole to the equator of the Earth is approximately10000 km, 1 km on the surface of the Earth subtends an angle of one centigon at the centre of the Earth. However the gon is rarely used.
The angle through which the torsion-head must be deflected was measured in centesimal divisions of the circle
{{cite book}}:ISBN / Date incompatibility (help)German:wurde die Größe der Drehung oben an der Drehwage in Hunderttheilen einer ganzen Umdrehung abgelesen (p. 147) [the amount of rotation at the top of the torsion balance was read in hundred parts of an entire revolution]
It hung on a ribbon torsion element with a knob on top, graduated in 100 parts.
The term "Celsius" was adopted instead of the more familiar "centigrade" because in France the word centigrade has customarily been applied to angles.
On the approximation of the laws of the Member States relating to units of measurement and on the repeal of Directive 71/354/EEC.
On most scientific calculators, this [the unit for angles] is set by the DRG key
Scientific calculators commonly have two modes for working with angles – degrees and radians