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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 .


	Contributed by: Michael Morrison
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Continued Fraction (Wolfram MathWorld)

"Instantly Periodic General Continued Fraction Representations of Square Roots" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/InstantlyPeriodicGeneralContinuedFractionRepresentationsOfSq/

Contributed by: Michael Morrison

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