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Play with the continued fraction:

Notice that it increases with

,

,

and decreases with

and

.

The numbers π, ϕ,

,

are given by the sequences

.

Contributed by: George Beck

Continued Fraction (Wolfram MathWorld)

Quadratic Surd (Wolfram MathWorld)

"Short Simple Continued Fractions" from the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/ShortSimpleContinuedFractions/

Contributed by: George Beck

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