“Mathematics is to nature as Sherlock Holmes is to evidence.” (Adam 3) This is especially the case when studying the golden ratio. The golden ratio, also known as the golden mean or the divine proportion, is a number found often in nature, sometimes even referred to as “God’s fingerprint”. It is approximately 1.618034. The golden ratio has been used in art since antiquity; it was used to build the famous Egyptian pyramids, as well as the Stonehenge. We know that artists like Leonardo da Vinci and Albrecht Durer used it in their paintings, and that it is used in constructing musical instruments.
In nature, we see it expressed often in the Fibonacci spirals that characterize the behavior of plants and animals. What does Fibonacci got to do with the golden ratio? Well, if you divide numbers in the Fibonacci sequence with their predecessor, you will come up with numbers that get closer and closer to the golden ratio.
Below you can see my attempt to find an equation for the Fibonacci spiral using the golden ratio , and the graph of it. Sadly, after finishing it I realized that Google had beat me to it, and already had similar graphs.
Source:
Adam, John A. Mathematics in Nature. Princeton: Princeton UP, 2011. Print.
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