Re: LOGO-L> Total Turtle Trip

[Chuck Shavit <CShavit@MagicSquare.com>]

Mike Doyle wrote:
> The Turtle has two capabilities:
> 
> To move in a positive or negative direction.
> To turn in a clockwise or anticlockwise direction.
> 
> The commands are, respectively:
> Forward (back) and
> Right (left)
> 
> The movement is expressed in arbitrary units.
> The turn is expressed as degrees of arc.
> 
> It follows that Turtle geometry implicitly relies upon a (conventional)
> understanding of a circle, i.e. as an arc described by a rotating point.
> That is to say that the Turtle has inbuilt the 'knowledge' developed
> through using a compass to draw and divide circles.
> 
> The turtle, however, cannot move in a circular arc. It can only move by
> 'step and turn', leading to procedures of the form:
> 
> To shape :sides
> Repeat :sides (forward 1 right 360/:sides)
> End
> 
> Which will draw a regular polygon.

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
---------------------------------------------------------------
Please post messages to the Logo forum to logo-l@gsn.org.  Mail
questions about the list administration to logofdn@gsn.org.  To
unsubscribe send    unsubscribe logo-l    to majordomo@gsn.org.