Re: [MATHEDCC] Why radians?

gdorner@HARPER.CC.IL.US
Mon, 01 Nov 1999 14:52:07 -0500

There was a brief article on the history of the radian by Robert J. Walker in
The Physics Teacher, V. 32, Oct. 1994. There is a bibliography of 17 items and
a discussion of mils and grads as measures of angles. There seems to be some
disagreement about whether Thoms Muis, a mathematician, or James Thompson, the
physicist, used the word radian first and at Dublin or Cambridge. The Greeks
really didn't have trigonometry in their geometry, but they used the chord
subtended when discussing angles. The Babylonians did the same and had tables
which were virtually based on radians.

The mil, used in artillery, is the angle subtended by 1/1600 of a right angle
and about that subtended by one meter at 1000 meters or about that subtended
by a yard at 1000 yards. In 1941, a report was published in AMM and in Math
Teacher entitled "The Mil as an Angular Unit and its Importance to the Army."
Does anyone know if the mil is still used in artillery? It was when my father
took ROTC in 1927-28. This mil is not the same as a circular mil which is the
area of a circle with diameter equal to 1 mil (0.001 inch) and which is used
in measuring the cross-sectional area of wire.

The grad or grad is one one-hundredth of a right angle.It has been around
since the early 19th century and apparently was introduced by D'alembert.

There were a number of other articles about the radian in the Physics Teacher,
especially in discussions about the metric system.

geo dorner

Martin Kalmar wrote:
>
> When students ask (not often enough) why do we need to measure angles in radians, I know of no other answer than it makes things very convenient in calculus. This is fine for my calculus students who can see what the derivatives of trig functions would look like without radians, but what other answer can I give my pre-calculus students?
>
> Does anyone know of other good reasons for using radians?
>
> Does anyone know the history of radian measure? Who first used it and why?
>
> Martin Kalmar
> Frederick Community College
> Frederick, Md.
> mkalmar@fcc.cc.md.us
>
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