Fibonacci's sequence is seen throughout nature, but it can be clearly seen in the Golden Ratio. The Golden Ratio or phi (the greek symbol picture below) is roughly equal to 1.618034. Fibonacci's Numbers play into the ratio when one takes a Fibonacci number and divide it by the previous Fibonacci number. The ratio is not always perfect, but is averaged to the Golden Ratio. The graph below shows the trend between the Fibonacci number and the ratio. For the first few terms, the ratio is either 1 or 2, but as the sequence goes on it appears to be coming to a limit of 1.618034 (as seen below).
The Golden Ratio is used in many aspects of life. It is most apparent though in architecture. The perfect rectangle is a 1x1.6, or the Golden Ratio. A rectangle with these dimensions is so eye appealing that it is referred to as the Golden Rectangle.
Works Cited:
1) "The Life and Numbers of Fibonacci." Plus.maths.org. Plus Math Magazine, n.d. Web. 09 June 2014. <http://plus.maths.org/content/life-and-numbers-fibonacci>.
2) "Painting by Numbers." IEEE Spectrum 47.3 (2010): 20-21. Scientiareview. Scientiareview. Web. 10 June 2014. <http://www.scientiareview.org/pdfs/208.pdf>.
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