In article 
<[email protected]>,
 Peter Nilsson <[email protected]> wrote:

> Keith Thompson <[email protected]> wrote:
> > 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.
> 
> Yes, but what is pi then?
> 
> > 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.
> 
> The formula: circumference = 2 x pi x radius is taught
> in primary schools, yet it's actually a very difficult
> formula to prove!

What's to prove?  That's the definition of pi.

rg
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