# Eggs are Eggs-actly Complex and Interesting

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….

Hi,

The first math equation was way above my pay grade. 🙂 But understood the second one perfectly. Loved it and had a good laugh as well.

A great post, and I really did enjoy reading it.

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Thanks for stopping by. I feel I can never go wrong if I invite Calvin and Hobbes to explain something for me.

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That math problem is pretty much how we approach most of life, taking simple problems and turning them into huge ones. Great post, Margie.

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Thanks! Just doing my best to improve your math skills…

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Very intriguing indeed, haha!

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I thought of you, Tien, when I wrote down the mathematical equation. I’m guessing, with your background, you would know how to solve it!

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My husband used to tell me that Physics use equations to explain and simplify (whatever). But, the Cartesian Oval looks complicated to get 0…

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Hi Amy – I guess it takes a certain mind to understand equations, and unfortunately that is not really how mine thinks!

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