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Egg Geometry Puzzle and Chick Embryos



Calling all eggheads:

I've visited a web site called "Chickscope" which deals mostly in images of
developing chick embryos.  In their EggMath section, they describe
mathematical formulae for plotting standard ellipses (a common dinosaur egg
shape) and Cartesian ovals (the shape of the chicken egg, for instance). 
The site also describes the hands-on methods for drafting the shapes using
only a sheet of paper, a cardboard, wood or cork surface, two pins, a bit
of string, and a pencil.  I was familiar with the ellipse drafting
technique, which works quite well.  However, I was not able to draw the
Cartesian oval using the method described, and succeeded only when I
"cheated" by using one pin and one disc as the "foci" for the loop of
string.

Question 1: Can you tell me how to draft a Cartesian oval using the two
pins, the loop of string, and the pencil?

Question 2: Are any non-avian dinosaur eggs known to have had this shape? 
If not, what animal originated it?  I've read that it began with
"cliff-nesting birds," but would appreciate more info.

Question 3: Can anyone point me to a source for photographs, drawings, or
images of chick embryos which are sufficiently detailed to show the gill
buds, the pre-ossification caudals (prior to the fusion into the
pygostyle), the three fingers (prior to the fusion into the wing elements),
or any other such embryonic details suggestive of the bird's ancestry?  The
site I mention lacks the necessary details.  Lennart Nilsson's vivid
"Odyssey of Life" documentary shows some of this imagery, but I am seeking
out a hard copy.

Eggmath: The Shape of an Egg: Cartesian Ovals can be found at
<http://chickscope.beckman.uiuc.edu/explore/eggmath/shape/descartes.html>.

-- Ralph Miller III     gbabcock@best.com 

 Favorite egg moment in film: "Rock and Roll Creation" performance from
"This is Spinal Tap."