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Unformatted text preview: Last Updated 120124 10:12 AM CSE 2011 Prof. J. Elder  28  Binary Recursion • Binary recursion occurs whenever there are two recursive calls for each nonbase case. • Example 1: The Fibonacci Sequence Last Updated 120124 10:12 AM CSE 2011 Prof. J. Elder  29  The Fibonacci Sequence • Fibonacci numbers are defined recursively: F = 0 F 1 = 1 F i = F i1 + F i2 for i > 1. (The “ Golden Ratio ”) Fibonacci (c. 1170  c. 1250) (aka Leonardo of Pisa) The ratio F i / F i ! 1 converges to " = 1 + 5 2 = 1.61803398874989. .. Last Updated 120124 10:12 AM CSE 2011 Prof. J. Elder  30  The Golden Ratio • Two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. ! is the unique positive solution to = a + b a = a b ....
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 Fall '11
 Elder
 Data Structures, Recursion, Fibonacci number, Golden ratio, Prof. J., Prof. J. Elder

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