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The Phoenix Function

Chris Niemann
Organization: Southwestern Illinois College
Department: Mathematics
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All irrationals can be approximated by fractions. For example, 22/7 is an often-used used approximation for Pi. My function, Phoenix, will deliver fractions of any desired level of accuracy. It does this by constructing a sequence of Partial Sequences. Vectors are used, where the top of the fraction is the first element and the bottom of the fraction is the second element. The Partial Sequences are arithmetic progressions of vectors. For illustration, the first 10 P.S.'s for Pi are delivered by the function, Phoenix. Then skipping around for half a dozen others. After that, Phoenix gives one P.S. for E.

*Applied Mathematics > Numerical Methods > Approximation Theory

Approximations, Fractions, 2D-Vectors, sequences of Partial Sequences, Arithmetic progressions
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FlightOfThePhoenix.nb (152.2 KB) - Mathematica Notebook