Gon (unit)

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• Gradian

History and name

The unit started in connection with the French Revolution in France as the grade, 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, 1/360 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 grade nouveau. In German, the unit was before now also called Neugrad (new degree) (whereas the standard degree was referred to as Altgrad (old degree)), also nygrad in Danish, Swedish 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 armed forces' artillery units have used the gon for decades. Today, the degree, 1/360 of a turn, or the mathematically more convenient radian, 1/2π of a turn (used in the SI system of units) is generally used instead.

In the 1970s –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: 50^g = 45°. 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.

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 (as 33+1/3 gon and 66+2/3 gon, respectively).

Almost the same way, in one hour (1/24 day), Earth rotates by 15° or 16+2/3 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: {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18}. However, there are only eight for 400: {1, 2, 4, 5, 8, 10, 16, 20}.