> The real question is "why degrees?" Degrees are a mistake.
> Initially, the Babylonian and Egyptian civilizations believed
> that it took 360 days for the Earth to revolve around the sun
> (one year), hence each degree was analagous to one day. This is,
> of course, an error.
With all due respect, I believe that it would be more accurate to
term 360 a "convenient approximation" than to call it a mistake.
The ancient astronomers had plenty of time for observation and
speculation, and they (particularly the Babylonians) were more aware
of the patterns of imperfection in the heavenly movements than
almost anyone alive today is.
> Does anyone know the history of radian measure? Who first used it
> and why?
A good research question. I'll bet the answer is in Cajori's history
of mathematical notations. Anyone have a quick answer on this?
BTW, another good book on the byways trigonometry can lead you to is
Eli Maor's new book "Trigonometric Delights" (Princeton University
Press, 1998).
> Does anyone know of other good reasons for using radians?
Several people have pointed out that calculations of arc length
require conversion to (or origination in) angle measures in radians.
This is somewhat of a circular argument (er -- no pun intended!),
since you cannot understand the idea of a radian until you have
swallowed the concept of arc length in the first place -- and
perceptive students might well be bothered by the idea of trying to
measure length along a curve in any naive fashion. Yet this is bread
and butter in Civil Engineering applications.
> 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.
Actually, by the time you are ready to study the derivatives of the
circular functions in calculus you should have moved beyond any
notion of angle associated with these functions. The proper way to
define sine and its cousins at this level is in terms of a point
moving along a unit circle. Of course, once again arc length comes
in here, but in a much more natural way.
Hmm, ask a good question, and see what a range of answers you get!
RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623
>>>> The plural of mongoose begins with p. <<<<
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