Re: LOGO-L> circular spiral

[George Mills <mills@softronix.com>]

I like the thought process of Yehuda's solution.
Which is simply to increase the diameter of the circle as you
go around. Those comfortable with using ARC would probably
grasp it nicely.

I think Yehuda may enjoy this slight refinement I made.

to spir 
for[rad 0 400 .2][arc2 5 :rad] 
end 

The above assumes MSWLogo due to the use of ARC2 which
moves the turtle along the arc rather than the ARC around
the turtle being in the center of the imaginary circle.
In other words ARC2 is doing the turning and moving along
an increasing diameter.

However, none of these solutions (including my orginal) is a
"mathematical" solution and fine for young students simply
trying to get an end result that "looks" right.

When possible I like starting with the formula for the theoretical
curve and then digitize it for computer display.  Much Like the
old poly (fd 1 rt 1) vs arc (sin/cos) debate.

Don't get mad now, this is what I'd try to get a high school student to
come up with. Now :ang is the true number of degrees you wish to rotate
the spiral for. You can make the 100 a parameter which would effect
the rate the spiral moves outward.

Note the function f_of_x is continuous and the spiral function
digitizes points along that curve defined by f_of_x. In otherwords if in a
high school level teaching situation it limits the confusing between
the math involved creating a function that creates the spiral curve and
how the computer draws it.

The thought process is simular to Yehuda's in that the radius of the
circle is increasing. The end result will look quite similar.

Notice also that I could change:

for [a 0 :ang 1] ~

to

for [a 0 :ang 10] ~

And every point would still be on the "same" curve, just the
number of dots we chose to connect along the curve changes.

to f_of_x :x
   output list ~
      :x/100 * cos :x ~
      :x/100 * sin :x
end

to spiral :ang
pu
for [a 0 :ang 1] ~
   [
   setpos f_of_x :a
   pd
   ]
end 

spiral 360  ;  1 loops
spiral 720  ;  2 loops
spiral 3600 ; 10 loops

Paul C Dench wrote:
> 
> Hello Megan
> 
> By the time you have all the suggestions you will be able to write a
> dissertation on the subject so I hesitate to add to your 'confusion'
> 
> George Mills' solution is a very elegant 'growth solution but not very
> transparent.
> 
> Yehuda's is too mathematical for my liking and even less transparent.
> 
> Marian Rosen's solution gets closer to the beginner Logo user thinking
> progress and taken a step further we could think of quarter circles, eighth
> circles etc or even smaller sectors as follows:
> 
> to spiral :size
> repeat 500[fd :size rt 20 make "size :size + .2]
> end
> 
> draw it by entering <spiral 1>
> 
> It's really no different than George's solution but easier to 'understand'.
> 
> Who'd have thought something as simple as a spiral would become an
> epistemological issue.
> 
> Paul Dench
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-- 
===============================================================
George Mills
email: mills@softronix.com
http://www.softronix.com
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