Английская Википедия:Gradian
Шаблон:Short description Шаблон:Redirect Шаблон:Redir Шаблон:Infobox unit
In trigonometry, the gradianШаблон:Sndalso known as the gon (Шаблон:Etymology), grad, or grade[1]Шаблон:Sndis a unit of measurement of an angle, defined as one-hundredth of the right angle; in other words, 100 gradians is equal to 90 degrees.[2][3][4] It is equivalent to Шаблон:Sfrac of a turn,[5] Шаблон:Sfrac of a degree, or Шаблон:Sfrac of a radian. Measuring angles in gradians is said to employ the centesimal system of angular measurement, initiated as part of metrication and decimalisation efforts.[6][7][8]Шаблон:Refn
In continental Europe, the French word centigrade, also known as centesimal minute of arc, was in use for one hundredth of a grade; similarly, the centesimal second of arc was defined as one hundredth of a centesimal arc-minute, analogous to decimal time and the sexagesimal minutes and seconds of arc.[9] The chance of confusion was one reason for the adoption of the term Celsius to replace centigrade as the name of the temperature scale.[10][11]
Gradians are principally used in surveying (especially in Europe),[12][7][13] and to a lesser extent in mining[14] and geology.[15][16]
Шаблон:As of the gon is officially a legal unit of measurement in the European Union[17]Шаблон:Rp and in Switzerland.[18]
The gradian is not part of the International System of Units (SI).[19][17]Шаблон:Rp
History and name
The unit originated in France in connection with the French Revolution as the Шаблон:Lang, 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, Шаблон:Sfrac 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 Шаблон:Lang. In German, the unit was formerly also called Шаблон:Lang (new degree) (whereas the standard degree was referred to as Шаблон:Lang (old degree)), likewise Шаблон:Lang in Danish, Swedish and Norwegian (also gradian), and Шаблон:Lang 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,[12][7][13] mining[14] and geology.[15][16] The French armed forces' artillery units have used the gon for decades.Шаблон:Citation needed Today, the degree, Шаблон:Sfrac of a turn, or the mathematically more convenient radian, Шаблон:Sfrac of a turn (used in the SI system of units) is generally used instead.
In the Шаблон:Nowrap1990s, most scientific calculators offered the gon, as well as radians and degrees, for their trigonometric functions.[20] In the 2010s, some scientific calculators lack support for gradians.[21]
Symbol
Шаблон:Infobox symbol Шаблон:Infobox 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, 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.
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 Шаблон:Sfrac gon and Шаблон:Sfrac gon respectively).
Conversion
Relation to the metre Шаблон:Anchor
Шаблон:Further Шаблон:See also
In the 18th century, the metre was defined as the 10-millionth part of a quarter meridian. Thus, 1 gon corresponds to an arc length along the Earth's surface of approximately 100 kilometres; 1 centigon to 1 kilometre; 10 microgons to 1 metre.[22] (The metre has been redefined with increasing precision since then).
Relation to the SI system of units Шаблон:Anchor
The gradian is not part of the International System of Units (SI). The EU directive on the units of measurement[17]Шаблон:Rp 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.[19] The previous edition mentioned it only in a footnote, which said the following:[23] Шаблон:Blockquote
See also
- Шаблон:Annotated link
- Шаблон:Annotated link (primarily military use)
- Шаблон:Annotated link
- Шаблон:Annotated link
- Шаблон:Annotated link
- Шаблон:Annotated link
- Шаблон:Annotated link (the "square radian")
Notes
References
External links
- Ask Dr Math
- Definitions of grade, gon and centigrade on sizes.com
- Dictionary of Units
- ↑ Шаблон:Cite web
- ↑ Шаблон:Cite book
- ↑ Шаблон:Cite web
- ↑ Шаблон:Cite book
- ↑ Шаблон:Cite web
- ↑ Шаблон:Cite book
- ↑ 7,0 7,1 7,2 Шаблон:Cite book
- ↑ Шаблон:Cite book
- ↑ Шаблон:Cite book
- ↑ Шаблон:Citation. On p. 42 Frasier 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.
- ↑ Шаблон:Citation
- ↑ 12,0 12,1 Шаблон:Cite book
- ↑ 13,0 13,1 Шаблон:Cite book
- ↑ 14,0 14,1 Шаблон:Cite book
- ↑ 15,0 15,1 Шаблон:Cite book
- ↑ 16,0 16,1 Шаблон:Cite book
- ↑ 17,0 17,1 17,2 Шаблон:Cite web
- ↑ Шаблон:Cite web
- ↑ 19,0 19,1 Шаблон:SIbrochure9th
- ↑ Шаблон:Citation
- ↑ Шаблон:Citation
- ↑ Cartographie – lecture de carte – Partie H Quelques exemples à retenir. Шаблон:Webarchive.
- ↑ Шаблон:SIbrochure8th
