Surface Area of an Egg

Date: 07/20/2002 at 22:10:46
From: Perry 
Subject: Surface area of an egg

How do I find the surface area of an egg?

Date: 07/26/2002 at 09:09:51
From: Doctor Nitrogen
Subject: Re: Surface area of an egg


Hi Perry.

After lengthy searches, I could not find one neat formula that would 
help you calculate the surface area of an egg. The problem is that 
there is a lot of research by mathematicians on the shape/surface area 
of an egg, and there are many different kinds of "ovals" that help to 
determine an egg's shape: "Cassini" ovals, "lemniscate" ovals (these 
are parts to something which is called a "higher plane curve"), etc.  
Also remember that there are different kinds of eggs: chicken eggs, 
ostrich eggs, reptile eggs, dinosaur eggs, etc.

An ellipsoid (something shaped like the Goodyear blimp) is kind of 
shaped like an egg.  There are two special symmetric cases, 
called "prolate" and "oblate", for which formulas exist.
You can find those formulas in our FAQ:

  http://mathforum.org/dr.math/faq/formulas/faq.ellipsoid.html

The general case is more difficult.  You can find an extended discussion
of it here:

  Surface Area of an Ellipsoid
  http://home.att.net/~numericana/answer/ellipsoid.htm#thomsen

At the Chickscope's EggMath site,

   http://chickscope.beckman.uiuc.edu/explore/eggmath/ 

you will find almost every conceivable geometrical fact about 
eggs.  But if you have an egg that doesn't seem to fit any of the
formulas at these sites, you can still come up with an approximation:

1. Find some yarn, or some speaker wire, or something like that, which
   won't stretch too much. 

2. Glue one end of the yarn at one end of the egg, and wind it 
   around until it covers the whole egg.  (You might want to use
   glue at some points along the way, to keep it from unraveling.
   You might also want to hard boil the egg, to keep it from breaking
   easily!)

3. When you've finished, cut the yarn so that you have a piece that
   just covers the egg.  The surface area of the yarn is the about
   the same as that of the egg. 
   
4. Measure the width of the yarn while it's pressed against the egg. 
   Unwind the yarn, and multiply that width by the length of the yarn,
   and you have the area - assuming that you were able to keep it from
   stretching while winding it around the egg. 

Hope this helps. 

- Doctor Nitrogen, The Math Forum
  http://mathforum.org/dr.math/