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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:   

  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:   

  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

  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  The term may have been used in the modern sense in the unpublished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   

  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
  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  

  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   
Associated Topics:
High School Definitions
High School Euclidean/Plane Geometry
High School Geometry
Middle School Definitions
Middle School Geometry
Middle School Terms/Units of Measurement
Middle School Two-Dimensional Geometry

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