Grad as a Measure of an Angle
Date: 03/20/2002 at 13:39:52 From: Evelyn Benoit Subject: Grad as a Measure of an Angle I would like more information about the grad. I know it is 1/400 of a full rotation and may have been used by the British military. I would like to know more about its origins, its use in the past, and whether (and how) it is used now. Some of my students have also looked and have been unable to find more information. Thank you, Evelyn Benoit
Date: 03/20/2002 at 17:00:13 From: Doctor Peterson Subject: Re: Grad as a Measure of an Angle Hi, Evelyn. There is some information about it in Russ Rowlett's _How Many?_, a dictionary of units listed in our FAQ: http://www.unc.edu/~rowlett/units/dictG.html grad or grade or gon (g or grd) a unit of angle measurement equal to 1/400 circle, 0.01 right angle, 0.9 degrees, or 54'. This unit was introduced in France, where it is called the grade, in the early years of the metric system. The grad is the English version, apparently introduced by engineers around 1900. The name gon is used for this unit in German, Swedish, and other northern European languages in which the word grad means degree. Although many calculators will display angle measurements in grads as well as degrees or radians, it is difficult to find actual applications of the grad today. There is also a little information in Jeff Miller's Earliest Uses of Words of Mathematics, also listed in our FAQ: http://jeff560.tripod.com/g.html GRAD or GRADE originally meant one ninetieth of a right angle, but the term is now used primarily to refer to one hundredth of a right angle. Gradus is a Latin word equivalent to "degree." Nicole Oresme called the difference between two successive latitudines a gradus (Smith vol. 2, page 319). The OED2 shows a use of grade in English in about 1511, referring to one-ninetieth of a right angle. The OED2 shows a use of grade, meaning one-hundredth of a right angle, in 1801 in Dupre Neolog. Fr. Dict. 127: "Grade .. the grade, or decimal degree of the meridian." The term may have been used in the modern sense in the unpublished French Cadastre tables of 1801. In 1857, Mathematical Dictionary and Cyclopedia of Mathematical Science has: "The French have proposed to divide the right angle into 100 equal parts, called grades, but the suggestion has not been extensively adopted." Searching for other references, I found these: NIMA: Datums, Ellipsoids, Grids, and Grid Reference Systems http://cartome.org/nima-grids.htm Some foreign produced maps may use the centesimal (decimal) system of angular measurement (the division of a full circle into 400 grads). A grad (or gon) is divided into 100 centigrade (grad minutes), and each centigrad into 100 deci-milligrads (grad seconds). ... Geographic coordinates are given in terms of angular measurement, usually in degrees, minutes, and seconds but occasionally in grads. Gregor Shapiro helped me find this one: Silva: General Compass InformationReference Systems http://www.silva.se/outdoor/products/comp_general.htm Graduation Normal graduation is 360o. For Scandinavian countries 400 gon is also used. Military graduation 6400' or 6300' (Sweden). Often both 360o and 6400' are used, i.e. double graduation. That's all I've managed to find. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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