The Fibonacci Spiral and the Fibonacci Sequence

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This Demonstration draws an approximation to the golden spiral using the Fibonacci sequence. Squares are combined to form rectangles and quarter circles are drawn inside the squares to approximate the spiral. The ratio of the dimensions of a rectangle is the ratio of a pair of consecutive Fibonacci numbers. That ratio approaches the golden ratio, . Toggle the "show squares" button to see the squares.

Contributed by: Justin Lee (February 2019)
Open content licensed under CC BY-NC-SA


This was a project for Advanced Topics in Mathematics II, 2018–2019, Torrey Pines High School, San Diego, CA.


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