The Fibonacci Sequence
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In number theory a very famous sequence of numbers is the Fibonacci sequence. It has the form 1, 1,2,3,5,8 ..., where each subsequent number in the sequence is formed by adding together the two previous numbers. The Fibonacci sequence has many interesting properties and connections with art forms, nature and elsewhere and can be found through the Golden Ratio, otherwise known as Phi, or <D. Topics include identities of the sequence, which lead to a discussion on the Bilinear Index Reduction Formula, the Golden Ratio and its applications, the logarithmic spiral and the Golden Rectangle. This is a study of applications of the Fibonacci sequence, as we" as the recursive formula of the sequence itself. It results in a greater knowledge of the sequence and an understanding of how a mathematical sequence is incorporated in real life, how the numbers appear in nature and it gives the reader an understanding and appreciation of the multiple layers of complexity inherent in a numerical sequence.