# Gon

Physical unit
Unit name Gon
Unit symbol ${\ displaystyle \ mathrm {gon}}$
Physical quantity (s) Flat angle
Formula symbol Preferred angle names are Greek lowercase letters ( ) ${\ displaystyle \ alpha, \ beta, \ gamma ...}$
dimension ${\ displaystyle {\ mathsf {{\ frac {L} {L}} = 1}}}$
In SI units ${\ displaystyle \ mathrm {1 \, gon = {\ frac {\ pi} {200}} \; rad \ approx 0 {,} 0157 \; rad}}$
Named after Greek γωνία , gōnía = "angle, corner"
Derived from Full angle

The gon ( Greek γωνία gōnía , German 'angle, corner' ) is an auxiliary unit of measurement for specifying the angular width of plane angles, which could only be established in surveying . "Gon" is used as the unit symbol. A gon is defined as the four hundredth part of the full angle , i.e. H. 1 full angle = 400 gon = 360 °. The usual valid subdivisions are the centigon ( cgon ) and the milligon ( mgon ). The gon is not an SI unit , but a legal unit in the EU countries and Switzerland . It used to be called grads and was identified by a superscript small "g" (" g "). However, since January 1, 1980, the term  Neugrad '' is no longer provided in Germany.

## application areas

The gon is used in particular in surveying ( geodesy ) as well as in mine excavation in mining. It is the central starting point for robotics and automation technology , as the majority of the stepper motors used here work with 200 steps per full circle.

## Conversion into other angular units

${\ displaystyle 1 \, \ mathrm {gon} = {\ frac {1 \, \ mathrm {full angle}} {400}} = {\ frac {2 \ pi \, \ mathrm {rad}} {400}} = {\ frac {\ mathrm {360 ^ {\ circ}}} {400 ^ {\, \,}}} = 0 {,} 9 ^ {\ circ}}$

## separations

### Centigon

A centigon (cgon) (outdated notation: centigon ) is the hundredth part of a gon. The following applies to the centigon: 1 cgon = 32.4 " . It corresponds roughly to the resolution of the human eye or the measuring accuracy of a sextant or a small measuring table .

### Milligon

A milligon (mgon) is the thousandth part of a gon. The following applies to the Milligon: 1 mgon = 3.24 ″.

In most surveying theodolites, the milligon is the decimal point to which the horizontal directions and vertical angles can be read (storage is usually carried out at 0.1 mgon in order to avoid rounding errors).

### New minutes and new seconds

As a grad , the gon was previously divided into 100 new minutes of 100 new seconds each. These units are no longer permitted in Germany since January 1, 1978. They can still be used in Austria, but not with an SI prefix .

A new minute (1 c was previously written for this ) corresponds to a centigon (1/100 gon). A new second (previously 1 cc was used for this ) corresponds to 1 / 10,000 gon = 0.1 mgon.

1 c = 100 cc
1 g = 100 c = 10,000 cc
 1 c = 0.54 ′ 1 ′ = ${\ displaystyle {\ tfrac {10 \, 000} {5400}} \, {} ^ {\ mathrm {c}} = {\ tfrac {50} {27}} \, {} ^ {\ mathrm {c} } = 1 {,} {\ overline {851}} \, {} ^ {\ mathrm {c}}}$ 1 cc = 0.324 ″ 1 ″ = ${\ displaystyle {\ tfrac {1 \, 000 \, 000} {324 \, 000}} \, {} ^ {\ mathrm {cc}} = {\ tfrac {250} {81}} \, {} ^ {\ mathrm {cc}} = 3 {,} {\ overline {086 \, 419 \, 753}} \, {} ^ {\ mathrm {cc}}}$

The gon allows each of the four quadrants to be assigned a separate hundreds digit:

 0 ° = 0 gon 90 ° = 100 gon 180 ° = 200 gon 270 ° = 300 gon 360 ° = 400 gon

This simplifies the manual setting of right angles (100 gon or 300 gon) and straight angles (200 gon). The latter are of great importance in connection with redundant precision measurements with theodolites in two telescope positions , because gross measurement errors in the visual partial circle reading of the horizontal circle and vertical circle are easy to recognize, since the differences between the two respective readings must be 200 gon and are therefore only in the hundreds may distinguish.

In addition, the gon was subdivided decimally from the beginning, while the degree was subdivided sexagesimally , but is now usually also subdivided decimally. However, the degree is usually not combined with unit prefixes.

A major disadvantage is that important angles such as 30 ° and 60 ° must be expressed as fractions ( 33 13 and 66 23 gon).

## history

Compass with 400 gon graduation and conversion table

The Metrifizierung - so the conversion to the metric system - was in the 1790s in France started and required a precise level measurement . The Peru-Lapland measurement from 1735 to 1740 for the definition of a length measure with exactly 10,000,000 meters from the equator to the pole did not bring the desired results, but at least made the problem of flattening the earth clear. Jacques Cassini and Jean Dominique Comte de Cassini carried out the Nouvelle Triangulation de la France until 1793 and the first standard meter was defined in 1795 as the ten millionth part of an earth meridian quadrant . For this purpose, a new graticule was developed so that the full angle corresponded to 400 units of grade nouveau (grads) and one unit (1 gr ) measured exactly 100 kilometers at the equator. The term grads served to distinguish it from standard grade (fr. Degré ), who then old degrees was called. In France, the Gon is also called grade indicated (symbol: superscript gr) and English as a degree . The name Gon , which has been standardized in ISO 31-1 for a long time, is intended to eliminate this confusion. Since then, the terms Altgrad, Neugrad ( g ), Neuminute ( c ) and Neusekunde ( cc ) have been obsolete.

For a while, attempts were made to establish the gon as a general measure of angles in technology . The advantages of the decimal quarter circles, however, were of little importance in other areas, so that it could not prevail. The gon is only established in geodesy , theodolites usually have a scale in gons.

## Others

A term analogous to " radians " or " degrees " is rarely used in connection with the gon. Occasionally the terms "gon measure" or "geodetic angle measure" are used.

1. The conversion factors between old minutes and new minutes also correspond to those between nautical miles and kilometers . This is simply because the equator due to the definition of the nautical mile as a minute of arc on the equator just and due to long nautical miles of the definition of the meter 40-Millionster part of the circumference of the earth (and this is just the equatorial length) of the equatorial 40000 km ( ) Long${\ displaystyle 60 '\ cdot 360 ^ {\ circ} = 21600}$${\ displaystyle 40000 = 100 {} ^ {\ mathrm {c}} \ cdot 400 \, {gon}}$