Melody Ables sends us this awesome collage with her covering text – ‘A Fibonacci spiral approximates the golden spiral; unlike the “whirling rectangle diagram” based on the golden ratio, above, this one uses quarter-circle arcs inscribed in squares of integer Fibonacci-number side, shown for square sizes 1, 1, 2, 3, 5, 8, 13, 21, and 34.
Approximate logarithmic spirals can occur in nature (for example, the arms of spiral galaxies). It is sometimes stated that spiral galaxies…See More
Photo: Melody Ables sends us this awesome collage with her covering text - 'A Fibonacci spiral approximates the golden spiral; unlike the "whirling rectangle diagram" based on the golden ratio, above, this one uses quarter-circle arcs inscribed in squares of integer Fibonacci-number side, shown for square sizes 1, 1, 2, 3, 5, 8, 13, 21, and 34.

Approximate logarithmic spirals can occur in nature (for example, the arms of spiral galaxies). It is sometimes stated that spiral galaxies and nautilus shells get wider in the pattern of a golden spiral, and hence are related to both φ and the Fibonacci series. In truth, spiral galaxies and nautilus shells (and many mollusk shells) exhibit logarithmic spiral growth, but at a variety of angles usually distinctly different from that of the golden spiral. This pattern allows the organism to grow without changing shape. Approximate logarithmic spirals are common features in nature; golden spirals are one special case of these.'
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