Origin of RadiansDate: 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_: http://www.unc.edu/~rowlett/units/dictR.html 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_: http://www.pballew.net/arithme8.html#radian - Doctor Sarah, The Math Forum http://mathforum.org/dr.math/ |
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