Gon (unit)

In trigonometry, the gradian, also known as the gon is a unit of measurement of an angle, defined as one hundredth of the right angle; , there are 100 gradians in 90 degrees. It is equal to of a turn, of a degree, or of a radian. Measuring angles in gradians is said to employ the centesimal system of angular measurement, started as part of metrication and decimalisation efforts.
In continental Europe, the French word centigrade, also known as centesimal minute of arc, was in use for one hundredth of a grade; in almost the same way, the centesimal second of arc was defined as one hundredth of a centesimal arc-minute, the same as decimal time and the sexagesimal minutes and seconds of arc. The chance of confusion was one reason for the adoption of the term Celsius to replace centigrade as the name of the temperature scale.
Gradians are mostly used in surveying (especially in Europe), and to a lesser extent in mining and geology.
the gon is officially a legal unit of measurement in the European Union and in Switzerland.
The gradian is not part of the International System of Units (SI).
History and name
The unit started in connection with the French Revolution in France as the , along with the metric system, hence it is every once in a while referred to as a metric degree. Due to confusion with the existing term grad(e) in some northern European countries (meaning a standard degree, of a turn), the name gon was later adopted, first in those areas, and later as the international standard. In France, it was also called . In German, the unit was before now also called (new degree) (whereas the standard degree was referred to as (old degree)), also in Danish, Swedish and Norwegian (also gradian), and 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 armed forces' artillery units have used the gon for decades. Today, the degree, of a turn, or the mathematically more convenient radian, of a turn (used in the SI system of units) is generally used instead.
In the 1990s, most scientific calculators offered the gon, as well as radians and degrees, for their trigonometric functions. In the 2010s, some scientific calculators lack support for gradians.
Symbol
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, almost the same to a degree sign: 50g = 45deg.
A metric prefix is sometimes used, as in "dgon", "cgon", "mgon", representing 0.1 gon, 0.01 gon, 0.001 gon respectively. Centesimal arc-minutes and centesimal arc-seconds were also represented with superscripts c and cc, respectively.
Advantages and disadvantages
Each quadrant is assigned a range of 100 gon, which reduced recognition of the four quadrants, as well as math involving perpendicular or opposite angles.
{|
|-
|align="right"| 0deg ||align="center"| = ||align="right"| 0 gradians
|-
|align="right"| 90deg ||align="center"| = ||align="right"| 100 gradians
|-
|align="right"| 180deg ||align="center"| = ||align="right"| 200 gradians
|-
|align="right"| 270deg ||align="center"| = ||align="right"| 300 gradians
|-
|align="right"| 360deg ||align="center"| = ||align="right"| 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 30deg and 60deg in geometry must be expressed in fractions (as gon and gon, respectively).
Almost the same way, in one hour ( day), Earth rotates by 15deg or gon (see also decimal time). These observations are a result of the fact that the number 360 has more divisors than the number 400 does; especially, 360 is divisible by 3, while 400 is not. There are twelve factors of 360 less than or equal to its square root: . However, there are only eight for 400: .