Wassenaar (egg) curve

quartic

An often raised question is that about the oval curve that describes an egg.
Above formula gives, for certain values for the parameter a, a rather good presentation of an egg. I call the curve the egg curve or the Wassenaar (egg) curve.

Starting with an ellipse, with proper measures, make one end smaller than the other one.
This leads 1) to a quartic function.
When taking linear transformation into account, parameters b (roundness) and c (difference between the ends) vanish into one parameter a (b/c) in above equation.

A good chicken egg has a value for parameter a between 5 and 6.

Other curves that can be used as an approximation of an egg are:

Ken Sasaki wrote a paper for the American Journal of Physics about the spinning possibilities of several egg-shaped forms 2).

 


notes

1) Via y = √(1 - bx2) + c x2

2) The paper is named: 'Spinning eggs - which end will rise?'.