Re: LOGO-L> Total Turtle Trip

[Chuck Shavit <CShavit@MagicSquare.com>]

Brian Harvey wrote:
> 
> Chuck Shavit <CShavit@MagicSquare.com> writes:
> >To illustrate: if the turtle movement mode is to move on a circle of radius
> >100, then FORWARD 100 would draw 1/(2*pi) of the circle's perimeter.
> 
> I'm not sure I like this.  From the user-interface point of view, it's
> modeful instead of modeless -- that is, the user has to remember some past
> history in order to know what FORWARD means right now.

I agree with you that it's a matter of taste.  I don't agree about the
modeless thing.  FORWARD is modal and its effect on the screen depends very
much on past history.  The behavior depends not only on the current
turtle's position and the direction, but also on its color, pen up/down,
width, and other variables depending on the implementation.  So one  might
look at curvature as a natural extension of the modal nature of FORWARD.
And then, one might not.  Ask anyone who skinned a cat.

> And I think that straight-line motion *should be* privileged.  If you look
> at the discussion of curvature in your calculus class, it is defined in
> terms of (limits of) straight line motions.  So to build the curvature
> into FORWARD seems to me to beg the question.

Again, Brian, it depend on which side of the curve you are.  When you stand
on our beloved planet Earth a draw a straight line in the sand, it's really
a segment of an arc.  And as Einstein toughts us as long ago as 1915, even
a straight line in outer space is part of an arc.  And vice versa, as you
point out.

Are we nitty gritty or what.

But more seriously, curved FORWARD has, IMO, an important goal in
introducing non Eucleadian geometry at a very intuitive way, and at a
relatively young age.  I'm not an educator, but I have done it with some
surprising results with my own kids.

Chuck

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