A Golden Opportunity: Mathematical Patterns in Nature
Jay Connor
The Fibonacci sequence has intrigued mathematicians, artists, scientists and philosophers for centuries. The Fibonacci sequence comprises of the numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on … where each number is the sum of the two numbers that precede it.
Discovered by Leonardo Fibonacci in around 1200, the sequence ties in closely with the Golden Ratio since the ratio of any two successive Fibonacci numbers is very close to the Golden Ratio.
The Golden Ratio is also known as Phi, 𝜑 , and it approximates to 0.61803... Similar to pi, phi is an irrational number; that is its decimal digits carry on forever, with no repeating pattern.
Phi has many alternative names including the golden mean, divine proportion and the golden section.
Today, its patterns and ratios can be seen throughout many biological systems and inanimate objects. Fibonacci numbers can be thought of as Nature’s numbering system.
Leonardo of Pisa was known as the greatest European mathematician of the middle ages. He has long been associated with the Golden Ratio. In addition, he is famous for introducing the decimal number system into Europe, the additive and subtractive rules into the Roman numeral system and the term ‘algorithm’.
Petals
The number of petals in a flower consistently follows the Fibonacci sequence. Famous examples include the Lily, which has three petals, Buttercups, which have five, and the Daisy's thirty four. ‘Phi’ appears in petals on account of the ideal packing arrangement as selected by Darwinian processes. Each petal is placed at 0.618034 per turn (out of a 360° circle), allowing for the best possible exposure to sunlight and other factors. The Fibonacci sequence can also be seen in the way tree branches form or split. A main trunk will grow until it produces a branch, which creates two growth points. Then, one of the new stems branches into two, while the other one lies dormant. This pattern of branching is repeated for each of the new stems. Root systems and even algae show this pattern. Tree Branches
The Buttercup’s five petals.
A diagram showing the Fibonacci sequence in trees’ branches.
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