The Golden Ratio ,Golden Section,  or Divine Proportion, most often designated by the Greek letter, Phi          is one of the most elegant constructions in mathematics,  with a numerical value of approximately 1.618.

Also known as extreme and mean ratios, the golden ratio is expressed below as DC/CE = DE/DC.  When the square ABCD is inscribed in the rectangle AFED it results in another rectangle of the same proportions, BCEF.  If one inscribes a square HGEC in that rectangle, it results in another rectangle BFGH, and so on ad infinitum.  

However, from the artist’s point of view, it is the Golden Spiral that holds the most interest.  The spiral is constructed by connecting the corners of the squares as shown above.  This Logarithmic spiral (or equiangular spiral) continues to an infinite point.  Note that I place an object over the spiral's terminal point to avoid the temptation of attempting a graphic representation of the infinite.

Although the ratio was known to Euclid, Raphael, Descartes and others, much of the early research on this subject, especially the spiral, was done by the Swiss mathematician Jakob Bernoulli.  

So taken was he with the spiral that he ordered that when he died, one be placed on his grave marker.  A spiral was so placed, but alas, it was the less interesting Archimedean spiral.


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