Re: parametric: x = cos(t), y = sin(t)

In article <see-3F8102.10530107122007@[EMAIL PROTECTED]
>, Barb Knox
<see@[EMAIL PROTECTED]
> wrote:

> In article <061220071507321524%plsperry@[EMAIL PROTECTED]
>,
>  Paul Sperry <plsperry@[EMAIL PROTECTED]
> wrote:
> [SNIP]
> 
> > So, in my view, it is improper or, instead, meaningless to say "Let t
> > be angle between lines M and N" (although I'll confess to doing so at
> > every op****tunity). Also, it is awkward to properly state things like
> > "There are 2*Pi radians in a circle" - never mind the fact that there
> > are _no_ radians in a circle - or like "The sum of the angles of a
> > triangle is Pi radians".
> > 
> > I guess I am asserting that there is no such thing as an angle (how
> > many angles can dance on the head of a pin?). At least I have never
> > seen a definition that I found satisfying. In any case, it doesn't
help
> > to swap off one word - "angle" - for another - "inclination".
> > 
> > ...So there!
> 
> I guess I don't (yet) see the difficulty with the definition that an 
> angle between 2 rays with a common origin is the length of the interior 
> arc produced by the rays' intersection with the unit circle centred on 
> that common origin.
> 
> This handles the cases of an angle having zero radians (a degenerate 
> arc), a complete circle having 2 pi radians, and the sum of the angles 
> of a triangle being pi radians.
> 
> What am I missing?

Well, OK. The use of "interior angle", is a little vague.  There is
also the problem of orientation - is the angle Pi/4 or 7Pi/4 (or
-Pi/4)?

Defining an angle to be a length (whatever _that_ may be) seems counter
intuitive to me but that's alright.

I wonder what one does in "real world" situations where there are units
associated with lengths. ("How far is it from here to the grocery
store?" "Oh, about 5.63.") I guess one must require unitless "lengths"
or else two lines would form different angles depending on whether our
unit circle has a radius of one foot or one mile.

Anyway, I didn't (and don't) intend to be taken too seriously in my
exegesis about angles. Thanks for taking the trouble to respond.

-- 
Paul Sperry
Columbia, SC (USA)