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anonymous

  • one year ago

We can relate the golden ratio to the lengths of line segments as follows. If we start with a line segment AB and locate point C on the segment such that....

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  1. anonymous
    • one year ago
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  3. ganeshie8
    • one year ago
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    For part \(a\), start with the proportion \(\dfrac{AB}{AC}=\dfrac{AC}{CB}\) |dw:1436258443492:dw| replacing \(AB\) by \(AC+CB\), the proportion becomes \[\begin{align}\dfrac{AC+CB}{AC}&=\dfrac{AC}{CB}\\~\\ 1+\dfrac{CB}{AC}&=\dfrac{AC}{CB}\\~\\ \dfrac{CB}{AC}&=\dfrac{AC-CB}{CB}\\~\\ \dfrac{ AC}{CB}&=\dfrac{CB}{AC-CB} \end{align}\]

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