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Unformatted text preview: 3 , 2 3 , 3 3 , 4 3 , …) 11. The Golden Ratio is a solution to the equation x x 2 1 = + . The number has been traced back to ancient Greek philosophers. It is represented by the Greek letter φ (phi). It’s exact representation is 1 5 2 + . It’s approximate value is 1.618. 12. The Golden Ratio is related to the Fibonacci numbers because it is seen in Binet’s formula for finding the Fibonacci numbers. Also, as the Fibonacci numbers get larger, the ratio of consecutive Fibonacci numbers appears to approach the Golden Ratio. 13. The Divine Proportion, The Golden Number, The Golden Section 14. A golden rectangle is a rectangle whose sides are in the proportion of the golden ratio. 15. A Fibonacci rectangle is a rectangle whose sides are consecutive Fibonacci numbers. Examples (not drawn to scale): 16. Some examples of gnomonic growth include tree rings and a chambered nautilus. 2 1 13 21 55 89...
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- Spring '08
- Math, Fibonacci number, Golden ratio, Jacques Binet