Precisely and Eggs-actly

The codfish lays ten thousand eggs,
The homely hen lays one;
The codfish never cackles,
To tell you when she’s done;
And so we scorn the codfish,
While the humble hen we prize;
Which only goes to show you,
That it pays to advertise.
(Author Unknown)

A Hen’s Egg is a pretty interesting thing. Fragile enough to allow a baby bird to peck through it, it is also strong enough to protect the contents because it employs the arch. (Egg layers knew about arches before humans did…)

The shape of an egg is very complex. It isn’t a circle, it isn’t an oval. It is quite simply egg-shaped. Which makes it very hard to draw. A circle shape is pretty easy to construct with a simple compass. An oval is harder to draw, but at least it has two lines of symmetry. But an egg – well there isn’t even a simple bit of mathematics to describe the profile of an egg, much less draw one.

I did find the equation for a Cartesian Oval, and it looks like this:
4a²m²((c-x)²+y²)-(a²+m²c²-2cm²x+(m²-1)(x²+y²))²=0

Math was never my strong suit, but I think maybe the “=0″ part means this equals an egg… No, probably not.
All this math made me think of a Calvin and Hobbes Cartoon by Bill Watterson. Calvin asks Hobbes for help with his homework:

Calvin: Help me with this homework, OK? What’s 6+3?  
Hobbes: 6+3, eh? First we call the answer “Y” as in “Y do we care?” Now Y may be a square number, so we’ll draw a square and make this side 6 and that side 3. Then we’ll measure the diagonal.  
Calvin: I don’t remember the teacher explaining it like this.
Hobbes: she probably doesn’t know higher math. When you deal with high numbers, you need higher math.
Calvin: But this diagonal is just a little under two.
Hobbes: OK, here, I’ll draw a bigger square.

Of course, I can just open the picture of my egg in Photoshop, and instantly have a perfect egg shape to work with. But that kind of takes all the fun out of using a ruler and a compass and drawing a page full of intersecting and overlapping circles and then erasing all the lines that don’t contribute to the shape of an egg.

I think I would have enjoyed giving birth to my children much more if they had popped out as eggs….

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My Similar Egg Story: Red Lily Beetle – Some gooey insect eggs.