Spirals in Nature
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.
Read more about this topic: Golden Spiral
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“Man is endogenous, and education is his unfolding. The aid we have from others is mechanical, compared with the discoveries of nature in us. What is thus learned is delightful in the doing, and the effect remains.”
—Ralph Waldo Emerson (1803–1882)