Golden Ratio

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This series of excel interactive sheets look at the golden ratio.

The first two sheets investigate the ratio of each pair of consecutive terms in the Fibonacci series, and what happens to the ratio as the sequence tends to infinity. The following sheet shows different ways of looking at Pascal’s triangle and its link to the Fibonacci series.

The forth sheet introduced the golden rectangle and demonstrates that the rectangle is the sum of an infinite number of squares. Click “∑ squares” to continue to a subsequent sheet showing how this leads to the value for the golden ratio.

The fifth sheet looks at how a regular pentagon can produce a value for the golden ratio using trigonometry. Click “Continue” to be taken to a further sheet showing how the golden ratio in surd form can then be derived.

The final interactive sheet demonstrates how a continued fraction can be arranged to give a closer and closer value for the golden ratio.

Note
This program was designed by be viewed on a screen with a resolution of 1024 x 768. Users may have to adjust the resolution of their screen for the pages to display as was originally intended. The program uses macros which need to be enabled on users’ machine.

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