Instantly Periodic General Continued Fraction Representations of Square Roots
This Demonstration provides a way to instantly write a periodic general continued fraction representation of square roots. This can be used as a quick way to easily approximate the numerical value of square roots.
(As opposed to a general continued fraction, a simple continued fraction has all of its numerators equal to 1.)
The proof of this representation is quite simple; let . Then, , so and simplifying gives .