Re: LOGO-L> Total Turtle Trip

[George Mills <mills@softronix.com>]

Chuck Shavit wrote:
> 
> 
> Two comments, one cent each:
> 
>   * I do not think that the concept of  "turtle geometry" necessarily
> precludes "real" circles.  It so happened that the original Logo's
> implementation has FORWARD movements only along straight lines.  So this is
> a limitation of Logo and not of the concept of turtle geometry.
> 
>   * If you want your students to use the computer to visualize the
> definition of a circle (all the points that are equidistant from a given
> center), you don't have to use a polygon.  Another way would be to write a
> simple program that draws dots around a center: each step would go forward
> with the pen up, draw a dot, go back, and turn.  As the number of dots
> increases, the collection looks more and more like a circle.  When the dots
> are denser than the size of a pixel, you get a perfect circle -- or as
> perfect as you can get on a computer screen.
> 
> Chuck Shavit

This is also the same as calculating where each X,Y point is using sine
and
cosine. By using FD,BK,RT your letting Logo do the trig but actually do
a lot
more work. 

Since the number of "dots" needed for a solid circle is a function of
radius you need to take that into consideration as well. For example if
your radius is 1 you only need 4 dots).

This so happens to be what the ARC code I posted some time ago does and
what
the built in ARC does in UCB/MSWLogo.

I agree with you, I consider a "true" ARC function as part Turtle
Geometry.
I think Brian suggested something similar to your suggestion above
during
the last "Poly" thread. Which started another thread on FD 0.

The end result of a reasonable dense "Poly" will look very much the same
as the "Points On the Curve" method of course. But I think "Points On
the
Curve" method is more mathematically sound (because your at least your
on the
curve).

-- 
===============================================================
George Mills
email: mills@softronix.com
http://www.softronix.com
The www page contains some very powerful educational software.
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