Scaling Up, Scaling Down

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Section 3.1 Scaling Up, Scaling Down

When we think of proportional reasoning, one of the areas of mathematics where we can truly "see" it is geometry. The ancient Greeks used a very special proportion in their artwork as well as architecture, The Golden Ratio. This ratio seemed to be found in nature and was deemed pleasing to the eye. In fact, the Fibonacci sequence, $\left\{1,1,2,3,5,8,13, \ldots \right\}\text{,}$ has the interesting characteristic that the successive ratios of adjacent terms, $\frac{F_n}{F_{n-1}}\text{,}$ approach The Golden Ratio as $n \rightarrow \infty\text{.}$ Just like the Fibonacci sequence that is seen throughout nature, The Golden Ratio also seems to be present all around us.

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