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To: "MWForum" <mwforum@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
Subject: Re: oval question
From: "Mike Sandy" <mjsandy@xxxxxxxxxxxxxx>
Date: Fri, 9 Mar 2007 14:39:05 -0000

There are several "versions" of ovals.
Descartes' ovals take the form f*d1+g*d2=s
d1, d2 are the distances of a point on the curve to the two foci (as with an
ellipse)
f, g are rational numbers. I've taken f<1 and g=1.
s is a number fixed for a given curve.

The equation 2*d1+d2=s can be drawn as follows.
As for an ellipse, put 2 tacks into a sheet of paper.  Take a piece of
string length, s.
Tie one end to one tack. Insead of tying the other end to
the other tack as  for the ellipse tie it to a pencil and
then loop the string round the remaining tack.
The  pencil is tensioned against the string (as for an ellipse).
The string length is thus made up of 2 lengths of d1 and one of d2.
Mike

----- Original Message ----- From: "Russell, Ken" <krussell@xxxxxxxxxxxxxxx>
To: <mwforum@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
Sent: Thursday, March 08, 2007 6:29 PM
Subject: oval question



How would one write a procedure to create an oval in logo? I think it will
use a little trig in there (sin?), but I'm (really) unclear on the
concept.

Wikipedia has some interesting information, one point being that the term
oval is somewhat unclear. I'm thinking of a squished circle that is
symmetric on two axis.

If anyone can help, my student would appreciate it!

Thanks in advance.



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