[MWForum]Elliptical orbits for planets

[Dale Reed]

> to ellipse :s :e
> pd
> local "n
> make "n 0
> repeat 360[rt :n fd :s lt :n lt :n fd :s * :e rt :n make "n :n + 1]
> end
>
> I love it's simplicity.

Daniel, this exact code is on page 440 of "Turtle Geometry: The Computer as
a Medium for Exploring Mathematics" by Harold Abelson and Andrea diSessa,
1980.   Eighth paperback printing 1992.

"15.  The following program draws an ellipse with size parameter S and
eccentricity (1 + E) / (1 - E). It uses a variable, N, to keep track of when
to draw with high and when with low curvature.  Techniques to prove this
will be developed in chapter 3."

I do not know if this is an ellipse or only an ellipse wannabe.  Maybe
differentiating the equation of an ellipse to find the changing
slopes(curvature?) might be useful for understanding.

But what is really interesting to me is this exercise illustrates the
difference between modeling in the turtle world rather than the x-y
coordinate system that is most often used.  Katy and I have been developing
an understanding of how this simple formula works by walking across the
living room rug.  Looking at the world from an individuals point of view
rather than a more collectivist vision.

Deep philosophical/political/economic ramifications are at play here.  Logo
is for sure low level, high level, and every level in between.    Dale
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$ dale-reed@att.net    Seattle, Washington USA $