Re: sin x / x tends to 1...

Lee Rudolph <lrudolph@xxxxxxxxx> wrote:
> Now, as you suggest, a similarly elementary theory of arc
> length for non-polygonal curves is lacking. But all we
> *need* is a theory of arc length for arcs of circles!
> And there, our bright 15-year old will be charmed by
> the definition of length that comes out of the usual
> proof that the derivative of the area of a circle
> with respect to the radius is the circumference
> by reversing the roles of some definitions and some
> conclusions. (Of course the proof also works for
> circular sectors.) I call that quite adequately
> elementary, for appropriate values of "bright".

Perfect - that does it - thanks.

> Doing this for yer average freshstudent in the USofA
> would be a fish of a different kettle, unfortunately.

;-)

--
Dr Darren Wilkinson
mailto:d.j.wilkinson@xxxxxxxxxxxxxxx
http://www.staff.ncl.ac.uk/d.j.wilkinson/
.

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