Gradian
gon | |
---|---|
General information | |
Unit of | Angle |
Symbol | gon, ᵍ, grad |
Conversions | |
1 gon in ... | ... is equal to ... |
turns | 1/400 turn |
radians | π/200 rad ≈ 0.0157... rad |
milliradians | 5π mrad ≈ 15.71... mrad |
degrees | 9/10° |
minutes of arc | 54′ |
In
In continental
Gradians are principally used in surveying (especially in Europe),[15][7][16] and to a lesser extent in mining[17] and geology.[18][19]
As of May 2020,[update] the gon is officially a legal unit of measurement in the European Union[20]: 9 and in Switzerland.[21]
The gradian is not part of the International System of Units (SI).[22][20]: 9–10
History and name
The unit originated in France in connection with the French Revolution as the grade, along with the metric system, hence it is occasionally 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 regions, and later as the international standard. In France, it was also called grade nouveau. In German, the unit was formerly also called Neugrad (new degree) (whereas the standard degree was referred to as Altgrad (old degree)), likewise 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
In the 1970s –1990s, most scientific calculators offered the gon, as well as radians and degrees, for their trigonometric functions.[23] In the 2010s, some scientific calculators lack support for gradians.[24]
Symbol
◌ᵍ | |
---|---|
Gon | |
In DEGREE SIGN |
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°. A metric 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 superscripts c and cc, 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 |
Advantages and disadvantages
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 (as 33+1/3 gon and 66+2/3 gon respectively).
Conversion
Turns | Radians | Degrees | Gradians |
---|---|---|---|
0 turn | 0 rad | 0° | 0g |
1/72 turn | π/36 rad | 5° | 5+5/9g |
1/24 turn | π/12 rad | 15° | 16+2/3g |
1/16 turn | π/8 rad | 22.5° | 25g |
1/12 turn | π/6 rad | 30° | 33+1/3g |
1/10 turn | π/5 rad | 36° | 40g |
1/8 turn | π/4 rad | 45° | 50g |
1/2π or τ turn | 1 rad | approx. 57.3° | approx. 63.7g |
1/6 turn | π/3 rad | 60° | 66+2/3g |
1/5 turn | 2π or τ/5 rad | 72° | 80g |
1/4 turn | π/2 rad | 90° | 100g |
1/3 turn | 2π or τ/3 rad | 120° | 133+1/3g |
2/5 turn | 4π or α/5 rad | 144° | 160g |
1/2 turn | π rad | 180° | 200g |
3/4 turn | 3π or ρ/2 rad | 270° | 300g |
1 turn | τ or 2π rad | 360° | 400g |
Relation to the metre
In the 18th century, the
Relation to the SI system of units
The gradian is not part of the International 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 the CGPM, CIPM or BIPM." The most recent, 9th edition of the SI Brochure does not mention the gradian at all.[22] The previous edition mentioned it only in a footnote, which said the following:[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 approximately 10000 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.
See also
- Angular frequency – Rate of change of angle
- Milliradian – Angular measurement, thousandth of a radian (primarily military use)
- Harmonic analysis – Study of superpositions in mathematics
- Jean-Charles de Borda – French scientist and Navy officer (1733–1799)
- Repeating circle – type of angular measurement instrument, notably used for navigation
- Spread (rational trigonometry)– 2005 book reformulating plane geometry
- Steradian – SI derived unit of solid angle (the "square radian")
Notes
References
- ^ Weisstein, Eric W. "Gradian". mathworld.wolfram.com. Retrieved 2020-08-31.
- Springer-Verlag. p. 63.
- ^ "NIST Guide to the SI, Appendix B.9: Factors for units listed by kind of quantity or field of science". nist.gov. NIST. Archived from the original on 2017-04-17.
- ^ Patrick Bouron (2005). Cartographie: Lecture de Carte (PDF). Institut Géographique National. p. 12. Archived from the original (PDF) on 2010-04-15. Retrieved 2011-07-07.
- ^ "Gradian". Art of Problem Solving. Retrieved 2020-08-31.
- ^ Balzer, Fritz (1946). Five Place Natural Sine and Tangent Functions in the Centesimal System. Army Map Service, Corps of Engineers, U.S. Army.
- ^ ISBN 041298511X.
- ISBN 978-1-4381-0957-2.
- ISBN 9781548494957.
The angle through which the torsion-head must be deflected was measured in centesimal divisions of the circle
- ^ Ohm, Georg Simon (1826). "Bestimmung des Gesetzes, nach welchem Metalle die Contactelektricität leiten, nebst einem Entwurfe zur Theorie des Voltaischen Apparates und des Schweiggerschen Multiplikators" (PDF). Journal für Chemie und Physik. 46: 137–166. Archived from the original (PDF) on 23 May 2020.
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]
- ISBN 978-0-7803-1193-0.
It hung on a ribbon torsion element with a knob on top, graduated in 100 parts.
- ISBN 978-0-486-14497-9. Retrieved 2022-01-02.
- doi:10.1080/00963402.1974.11458078. On p. 42Frasier 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.
- Bibcode:1976nbs..reptU....M,
The term "Celsius" was adopted instead of the more familiar "centigrade" because in France the word centigrade has customarily been applied to angles.
- ^ ISBN 9783110845716.
- ^ ISBN 9780750649872.
- ^ ISBN 9780415889391.
- ^ ISBN 978-1-4822-6288-9.
- ^ ISBN 978-3-540-74671-3.
- ^ a b c "Directive 80/181/EEC". 27 May 2009. Archived from the original on 22 May 2020.
On the approximation of the laws of the Member States relating to units of measurement and on the repeal of Directive 71/354/EEC.
- ^ "941.202 Einheitenverordnung" (in German). Archived from the original on 22 May 2020.
- ^ ISBN 978-92-822-2272-0
- ISBN 9780827346758,
On most scientific calculators, this [the unit for angles] is set by the DRG key
- ISBN 9781847876287,
Scientific calculators commonly have two modes for working with angles – degrees and radians
- ^ Cartographie – lecture de carte – Partie H Quelques exemples à retenir. Archived 2 March 2012 at the Wayback Machine.
- ISBN 92-822-2213-6, archived(PDF) from the original on 2021-06-04, retrieved 2021-12-16
External links
- Ask Dr Math
- Definitions of grade, gon and centigrade on sizes.com
- Dictionary of Units