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Origin of Radians

Date: 05/27/2002 at 08:35:49
From: Natalie Bowlus
Subject: Origin of radians

I'm doing a project in math on radians and degrees and I was 
wondering where, exactly, did radians come from?  When did people 
start to use them in calculations?  Thanks for the help.

Date: 05/27/2002 at 12:23:17
From: Doctor Sarah
Subject: Re: Origin of radians

Hi Natalie - thanks for writing to Dr. Math.

From Russ Rowlett's _How Many? A Dictionary of Units of Measurement_: 

  radian (rad) 
  a unit of angle measure widely used in mathematics and science. 
  One radian is the angle at the center of a circle that cuts off 
  an arc of length equal to the radius. Since the circumference 
  equals 2 pi times the radius, one radian equals 1/(2 pi) of the
  circle, or approximately 57.295 779 degrees. Using radians to
  measure angles seems unnatural at first. However, when angles 
  are stated in radians the constant pi tends to disappear from 
  the equations, and this greatly simplifies calculation. 

  For example, the length of an arc is simply its radius 
  multiplied by its angular measure in radians, and the area 
  of a sector of a circle is simply its angular measure in 
  radians multiplied by half the square of the radius. 

  The radian was defined and named by James Thomson in 1873. 
  Thomson was a mathematics professor at Queens College, Belfast,
  Northern Ireland, and the brother of the famous physicist 
  William Thomson, Lord Kelvin.

And see Pat Ballew's _Math Words, and Some Other Words of Interest_: 

- Doctor Sarah, The Math Forum 
Associated Topics:
High School Conic Sections/Circles
High School History/Biography
High School Trigonometry

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