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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).
1) Via y = ± √(1 - bx2) + c x2
2) The paper is named: 'Spinning eggs - which end will rise?'.