# Blog Archives

## THE GOLDEN MEAN – APPLICATIONS

The Golden mean and Fibonacci numbers  have been used since the time of Ancient Greece, especially in the design of the Parthenon.  This system might have even been used by the Egyptians in building the pyramids.  It has been used by artists such as Leonardo da Vinci, Michelangelo,  Picasso,  Seurat,  Signac,  Hopper, and Mondrian.  Even musicians have used it in their works — Mozart, Beethoven (his 5th Symphony), Bach, Schubert,  Bartok,  Satie,  and DeBussy have all been thought to use the divisions.  An article in The American Scientist of March/April 1996 points out that many of Mozart’s sonatas can be divided into two parts exactly at the golden section point in almost all cases.  The Mathematics Teaching magazine in 1978 points out that Beethoven used the system.  It is even thought that Virgil structured the Aeneid in this way.

In architecture, the Golden Mean is a standard proportion for width in relation to height, in first story to second story buildings, in the sizes of windows.  Look at any three-story bank building for instance to see the proportion in use.  The College of Engineering at the California Polytechnic State University built the new engineering plaza based on the Fibonacci numbers.   Plaza designer Jeffry Gordon Smith said, “As a guiding element, we selected the Fibonacci series spiral, or golden mean as the representation of engineering knowledge. ” The United Nations Building in New York is supposedly built on a golden rectangle.

What is most interesting is the way Leonardo Da Vinci’s The Last Supper was composed.  The scene itself is based on two squares, with Christ in the center.  All converging lines lead to the vanishing point on the horizon line, his face.  The top of the windows lies at a golden section as do the outer edges of the side windows. Christ’s hands are at the golden section of half the height of the composition.  The figures are grouped in threes, in a series of four shapes, with Christ forming the fifth.  Application of the Fibonacci numbers includes:  1 table, 1 central figure, 2 side walls, 3 windows and figures grouped in 3’s, 5 groups of figures, 8 wall panels and 8 trestle legs,  13 individual figures.

Realizing how often the Golden Mean and Fibonacci numbers have been used in all forms of art, I tried it myself in writing a poem.  I admit the structure is a little different, but here’s what I came up with based on the number of syllables in each line:

NOW YOU TRY IT!