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# The Fibonacci Sequence, Research Paper Example

Pages: 2

Words: 485

Research Paper

The Fibonacci sequence is named after Italian mathematical Leonardo of Pisa, who is also known as Leonardo Pisano, Leonardo Pisano bogollo, Leonardo Bonacci, and Leonardo Fibonacci. Fibonacci was one of the West’s finest Middle Age mathematicians, by which I don’t mean that he was middle aged, I mean that he was working during the Middle ages.

The prevalence of the Fibonacci sequence in nature had long been recognized. For example, the number of petals on many flowers is a Fibonacci number. Lilies have 3 petals, buttercups have 5, some delphiniums have 8, and so it goes on, with some daisies have 34, 55 or 89 petals. The characteristic pattern of sees in the head of a sunflower is a result of the Fibonacci series, too, and is related to a mathematical constant called the golden mean, golden ratio, or golden number.

“A Fibonacci sequence is a sequence of numbers in which each number is the sum of the two preceding numbers (e.g. 1,1,2,3,5,8,13). Patterns exhibiting the sequence are commonly found in natural forms, such as the petals of flowers, spirals of galaxies, and bones in the human hand” (Shesso, 2007). The ubiquity of the sequence in nature has led many to conclude that patterns based on the Fibonacci sequence are intrinsically aesthetic and, therefore, worthy of consideration in design.

Fibonacci patterns are found in many classic works, including classic poetry, art, music, and architecture. For example, it has been argued that Virgi used Fibonacci sequences to structure the poetry in the Aeneid. Fibonacci sequences are found in the musical compositions of Mozart’s sonatas and Beethoven’s Fifth symphony. Le Corbuster meshed key measures of the human body and Fibonacci sequence to develop the Modulor, a classic system of architectural proportions and measurements to aid designers in achieving practical and harmonious designs.

Fibonacci sequences are generally used in concert with the golden ratio, a principle to which it is closely related. For example, the division of any two adjacent numbers in a Fibonacci sequence yields an approximation of the golden ratio. Approximations are rough for early numbers in the sequence but increasingly accurate as the sequence progresses. As with the golden ratio, debate continues as to the aesthetic value of Fibonacci patterns. Are such patterns considered aesthetic taught to believe they are aesthetic? Research on the aesthetics of the golden ratio tends to favor the former, but little empirical research exists on the aesthetics of non golden Fibonacci patterns.

The Fibonacci sequence continues to be one of the most influential patterns in mathematics and design. Consider Fibonacci sequences when developing interesting compositions, geometric patterns, and organic motifs and contexts, especially when they involve rhythms and harmonies among multiple elements. Do not contrive designs to incorporate Fibonacci sequences, but also do not forego opportunities to explore Fibonacci relationships when other aspects of the design are not compromised.

Reference

Shesso, R., (2007), Math for Mystics: from the Fibonacci Sequence to Luna’s Labyrinth.

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