Re: LOGO-L> Total Turtle Trip

[George Mills <mills@softronix.com>]

Your correct, there is nothing in the universe that can create
a perfect physical representation of a circle. But you can choose
between different approximations to get different properties.

The "equidistant from center" method has some nice properties the
"poly" method does not (assuming a finite number of points of course
on a finite precision machine).

TO CIRCLE :RADIUS :POINTS
REPEAT :POINTS [FD (:RADIUS * 2) * PI/360 RT 1]
END

TO DIFF
CIRCLE 100 90
SHOW POS
CS
ARC2 90 100
SHOW POS
END

DIFF
[99.124796 100.870126] <<<< See how far off POLY is
[100 100] <<<< ARC2 basically uses the "equidistant model"

The difference between working from the center versus the edge versus
being relative or absolute is not the point of this this thread.

Also note the error above is not due to the finite precision of
the computer.

Mike Doyle wrote:
> 
> In-Reply-To: <3.0.2.32.19971027214617.00a3b730@tiac.net>
> On Monday 27th at 21:46 Chuck Shavit <CShavit@MagicSquare.com> wrote:
> 
> > This last issue is related, I think, to what Mike Doyle was saying.  The
> > relation between MCIRCLE and a mathematical circle is somewhat fuzzy.
> > Mike's mistake, if I understand him correctly, is that he thought that
> > MCIRCLE is the only Logo-ish way to draw circles.  But maybe I missed
> > something in what Mike was saying.
> 
> I think perhaps you missed the bit from /Turtle Geometry/ and /Mindstorms/
> that defined Turtle geometry as the geometry of a movement and a turn. To
> my mind (in 1982) this implied that the one impossible construction in
> Turtle geometry is a circle.
> 
> I noticed that all circle procedures in this thread are written with the
> objective of producing a perceptual circle on the screen. The Logo
> instructions in no way define the operation of describing a circle as, say
> a child swinging a cocker (horse chestnut) on a string would. The Logo-ish
> way I prefer is that used in Geomland, a Euclidean geometry microworld,
> where the compass is admitted as a virtual instrument.
> 
> The interesting relationship between Turtle geometry and digital
> representation, on the one hand, and Euclidean geometry and analogue
> representation, on the other appears to have been buried by Turtle
> Geometers delight in crafting obscure notation.
> 
> I become increasingly concerned that the influence of mathematicians on
> the development of the use of computers in schools has been unhelpful.
> 
> Michael Doyle (aka Micheal O Duill)
> 37 Bright Street
> SKIPTON BD23 1QQ UK
> Tel/fax: +44 (0)1756 794601
> Email: mikedoyle@cix.co.uk
> 
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-- 
===============================================================
George Mills
email: mills@softronix.com
http://www.softronix.com
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