Print

Print


> From: Veoler <[log in to unmask]>
> Alex Fink wrote:
> > And for what it's worth, if you want to give a name to one of these circular
> > numbers, two pi is the most natural one (being the actual period of the
> > imaginary exponential, etc.); it's by historical accident that half two pi
> > is the one we've bestowed a name on.  Have you given thought to this?
> 
> Not really. I haven't worked with complex numbers in the polar form.
> But isn't that less concrete (i.e. less accessible to an illiterate
> people) than wheels and such things which uses half two pi?
> 
> --
> Veoler

I think this depends on the hypothetical peasant-engineer's perspective. If they want to know how far a wheel will travel for a single rotation based on the length of the spokes, that's roughly twopi x spoke length (i.e., 2pi-r). If they want to know how far a wheel will travel based on how wide it is, that's pi x widest point (i.e., pi-d). So either could be used (although 22/7 x widest point is more accurate, 44/7 x [spoke length + fudge factor]  is easier to measure).

-- Paul