ATM: Donut Math

FYI for ATMs with a mathematical interest,

While reading Amateur Telescope Making Vol.1 (1996 edition), I
was puzzled by an equation on page 225 in a chapter on Doughnut
Mathematics. It related the deviation of paraboloid from a sphere
using the equation:

y = -k * (x^4) / (R^3)

I had assumed that the correct formula would be something like

y = (x^2)/(2*R) - (R - sqrt(R^2 - x^2))

After playing around with MathCad for a while, it occured to me
to look at a series expansion of this last equation. It quickly
reduced to the first.

Cheers,
Larry G.