Re: RADIANS

[Jack Uretsky <jlu@HEP.ANL.GOV>]

Hi all-
        This wording is unfortunate because it does not distinguish
between degrees and radians.  Each is a fraction of a rotation (as is a
"grad"), and each can be expressed in terms of the ratio of arc length
to radius.  One obtains Kilmer's (correct) conversion factor by observing
that a degree is 1/360'th of a circle while a radian is 1/(2\pi)'th of a
circle (I use TeX notation).  The 1/(2\pi) is obtained by observing that
it is the ratio of the arc length of a circle to the length of the radius.
        I discuss some implications of the effect of choice of units on
derivatives of trig functions in chapters 7 and 8 of the calculus text
that I am writing.  See math.GM/0010065 in the Los Alamos preprint
archives for a discussion.
                                Regards,
                                        Jack
On Wed, 29 Nov 2000, Kilmer, Skip wrote:

> Two possibilities:
> 1. Degrees are no more of a "unit" than radians. Radians are ratios of arc
> length to radius. Degrees are fractions of a rotation.
> 2. The conversion factor (Mr. One) is 180 degrees/pi radians.
> I prefer the first.
> Skip