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If you have a piece of straightedge 121 centimeters long, how can you cut it into five pieces so that you can measure any integral centimeter distance of 1 to 121 centimeters.  You can only use once each smaller straightedge you cut during the measurement.  

For example, if you cut the straightedge into 1, 15, 25, 35, 45 cm. pieces, you can measure 41 cm. by using the 1, 15, and 25 cm straight edges together.  These three straightedges can also measure 39 cm. by combining the 15 and 25 cm straightedges, and subtracting 1 cm from it.

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Bits and Beyond ... 


The Golden Ratio, also known as the divine ratio or proportion, is a ratio known for its relevance to art and aesthetics.  This ratio is also present in a variety of natural phenomena, particularly in the growth patterns of plant and animal life.  Some of the examples are the spirals formed by nautilus shells, and the growth patterns of ferns.  The Golden Ratio was derived by the ancient Greeks.  It is an irrational number with a value of 1.618...  Since the ancient times, artists and architects discovered that by utilizing this ratio, one could create a feeling of aesthetics in their works.  Both the ancient Greeks and the ancient Egyptians used the Golden Ratio when designing their buildings and monuments.  An example of an ancient structure using this ratio is the Parthenon.  Artists such as Leonardo da Vinci and George Seurat used the ratio in their paintings. 


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