regulating lines #2 - Dynamic Symmetry and the Golden Section

'Dynamic symmetry' is the name Jay Hambridge (1867-1924) applied to his study of the use by the Greeks of mathematical and natural growth forms of nature in their design. His book explains his theories and gives 'Lessons' for the reader. The figures are taken from the his introduction and Lesson 2. (In figure 4, the ratio between the square and the rectangle derived from the radius of the diagonal of half the square is the golden section.)

The ratio of the Fibonacci Series was known in the Renaissance as the Golden Section or Ratio now called 'phi' (the Greek letter) or 6.18... It "... cannot be worked out arithmetically; but it can easily be obtained with nothing more than a compass and a straightedge." Peter Tompkins, Secrets of the Great Pyramid, p.190.

Artists tend to know about these ideas:

*About 10 years ago an art teacher casually mentioned the golden section, telling me it is a common organizing tool for artists. I have now heard this several times.

*On a tour of the Saint Gaudens National Historic Site, Cornish, NH, a guide mentioned that Maxwell Parrish, who often painted there, used the golden section. I can find no references to verify that memory. (Maybe I need to lay out regulating lines on his paintings!)

*Karyl M. Knee wrote a phd.thesis in 1966 on Byzantine icons which examines the use and history of dynamic symmetry from its development by the Egyptians to its use in Russian iconography. The thesis is on line.

*Luca Pacioli, author of the first book on accounting, was a mathematician. He taught Leonardo da Vinci. In 15o9, da Vinci illustrated Pacioli's book, De Divina Proportione, describing the 'golden ratio'. Leonardo da Vinci's painting, The Last Supper, uses the golden ratio as its organizing principle.

* French historian Charles Funck-Hellet analyzed the golden section in Renaissance paintings, unfortunately for me, in French. I have not found a translation.