"Strong typing vs. strong testing"

[RG]

In article <ln8w22euvp.fsf at nuthaus.mib.org>,
 Keith Thompson <kst-u at mib.org> wrote:

> "BartC" <bc at freeuk.com> writes:
> > "RG" <rNOSPAMon at flownet.com> wrote in message 
> > news:rNOSPAMon-20651E.17410012102010 at news.albasani.net...
> [...]
> >> Likewise, all of the following are the same number written in different
> >> notations:
> >>
> >> pi/2
> >> pi/2 radians
> >> 90 degrees
> >> 100 gradians
> >> 1/4 circle
> >> 0.25 circle
> >> 25% of a circle
> >> 25% of 2pi
> >>
> >> See?
> >
> > But what exactly *is* this number? Is it 0.25, 1.57 or 90?
> 
> It's approximately 1.57.
> 
> > I can also write 12 inches, 1 foot, 1/3 yards, 1/5280 miles, 304.8 mm and 
> > so 
> > on. They are all the same number, roughly 1/131000000 of the polar 
> > circumference of the Earth.
> 
> They aren't bare numbers, they're lengths (actually the same length).
> 
> > This does depend on the actual size of an arbitrary circle, but that seems 
> > little different from the choice of 0.25, 1.57 or 90 for your quarter 
> > circle.
> 
> The radian is defined as a ratio of lengths.  That ratio is the same
> regardless of the size of the circle.  The choice of 1/(2*pi) of the
> circumference isn't arbitrary at all; there are sound mathematical
> reasons for it.  Mathematicians could have chosen to set the full
> circumference to 1, for example, but then a lot of computations
> would contain additional multiplications and/or divisions by 2*pi.

http://www.math.utah.edu/%7Epalais/pi.pdf

rg