Re: LOGO-L> Ellipses

[Jeff <jeffr@mugc.cc.monash.edu.au>]

On Sat, 24 Oct 1998, Bill Kerr wrote:
> repeat 360[rt :n fd :s lt :n lt :n fd :s * :e rt :n  make "n :n + 1]
> ahead. If George or anyone else can explain how this procedure works then
> I'll have another look at it. I just give it to the year 8's and let them
> play with it; it's still fascinating without understanding it but, yes, I
> would like to understand it too.
Bill
this procedure is a variant of the ellipse procedure in Abelson&diSessa's
'Turtle Geometry'(MIT Press)
If you hadn't given it to Adam, I would've, as only the rarest would ever 
derive it for themselves. If you step through it, it reveals itself as an 
epicycle, which has a nice resonance, as epicyclic motion was very 
familiar to pre-copernican astronomers. It was the only way they had of 
describing planetary motion in a terracentric universe. Of course later, 
planetary motion came to be described as elliptical.

cheers

Jeff

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