The Shape of an Egg (completely off subjects)

Dear Tuners & Instruments Makers,

I thought you might appreciate this formula.

The formula plots the curve of an egg - one that actually looks like an egg - as long as you keep the b/a value around 3:1. It also has some possibilities in musical instrument design (I think). I've started a drum with an egg shaped head, but I'm wondering if this might have other applications....lute bodies, maybe?

The Formula:
x = (+/-)sqrt(abs((a*(b/a)**(y/(a+b))**2)-(a-y)**2))

Definition of Terms:

"x" is plotted for both + and - "y" and only plotted for the range y=0 to y=a+b.

0<=a and a<=b
(try a=b, a=1,b=2 a=1,b=3)

The (a-y)**2 will begin to exceed the first term when b/a gets much larger than 3/1. I'm not sure what the exact limit is. It's something I'm still trying to understand.

The basic form of the formula is the pythagorean theorem. Radials from the focus (a) are the "(a*(b/a)**(y/(a+b)" term. If an egg with a=1, b=2 (a total height of 3) is plotted in increments of .25, the radials at each step are the 12th root of 2 to the n (where n0 =0, n1=.25, etc.)

Robin Perry

Matter is energy and energy, space.
The Nothing is something 'neath a featureless face.

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