On Sun, 30 Oct 2005, Chuckk Hubbard wrote:
I should be writing math textbooks. What does anyone use this particular equality for?
it's used in the formula for computing logarithms and cartesian-to-polar.
given f(x) = sum of x^n for n from 0 upwards = 1/(1-x),
then its integral F(x) = sum of (x^n)/n for n from 0 upwards = -log(1-x)
And combining complex numbers with log, you get atan, a function that turns slopes into angles.
Chances are that your CPU computes log and atan by applying such formulas.
There are many many other applications. Because it's a very simple formula, chances are many people encounter that pattern in many different situations. The place where I've used it most is in Probability Theory (!!!).
Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju Freelance Digital Arts Engineer, Montréal QC Canada