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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. |
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