The Fibonacci Spiral and the Fibonacci Sequence

curve segments

9

show squares

golden ratio = 1.61803

ratio = 1.61905

difference = 0.00101363

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,

ϕ=1.61803…

. Toggle the "show squares" button to see the squares.

Details

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

External Links

Golden Ratio (Wolfram MathWorld)

Golden Spiral (Wolfram MathWorld)

Permanent Citation

Justin Lee

"The Fibonacci Spiral and the Fibonacci Sequence"
http://demonstrations.wolfram.com/TheFibonacciSpiralAndTheFibonacciSequence/
Wolfram Demonstrations Project
Published: February 15, 2019