Introduction
One of the most intriguing formulas which I encountered during my 12th grade was the continued fraction expansion of \tan x. It was given in a book on "Numerical Analysis" and was offered as an example of a formula which converges very fast (like something comparable to the Maclaurin series for \sin x and \cos x). However like the usual practice followed in mathematics textbooks it was offered without any proof or any
context. I checked the formula using calculator and was amazed with its speed of convergence. Just 10 terms were enough to give the result with an accuracy up to 10 decimals.
