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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:

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NOW YOU TRY IT!

 

 

 

 

 

 


 
 
 

 


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AN INTRODUCTION TO DESIGN, PART II

To continue the discussion of design principles, we turn to RHYTHM.  We can understand the use of rhythm in dance and music,but it is also important in the visual arts.  And it is common to human nature.  All we have to do is look around us to discover the RHYTHM in nature. The cycles of the seasons — the growth, production, death, and rebirth of the land is familiar to each of us.  Even the simplest one-celled organism has a rhythmic pattern that relates it to the complex world outside. Man’s own internal system demonstrates the rhythm of life. Music and the dance began with the simple rhythms of primitive man, as he beat patterns on animal skin drums and stamped out the rhythm with his feet.

These five basic principles of design (UNITY,  VARIETY, DOMINANCE,  BALANCE, AND RHYTHM) work together to form aesthetic wholes in any form of art: dance, drama, literature, music, or the visual arts. The major difference between art forms is the matter of timing. The musician and the writer can manipulate an audience over a period of minutes or hours, attracting our attention, building up suspense to a climax, and unfolding the denouement to our enthralled eyes or ears. The visual artist, however, places his entire composition before the eyes of the viewer all at one, and it is the knowledge and experience of the viewer that determines how much he gleans from it.  no one would leave a play in progress, but many walk by a painting with just a cursory glance. A work of visual art deserves the time and study necessary to discover the artist’s design – his plan of arrangement to achieve his total effect.

More on design principles later.

AN INTRODUCTION TO DESIGN – PART I

In any field of art, the first thing for the artist is his idea, or subject matter. After this comes the composition of his ideas to best achieve the effect wanted.  To do his planning, the artist must be aware of certain principles or rules to be followed. No matter if the field is visual art, dance, music, literature, or drama; we still see the same principles at work.  These are not considered to be rules arbitrarily made up by a teacher – they are basic to the human condition. An understanding of these principles is inherent in good art, whether you are an observer or a doer.

For example, it is a psychological truth in human nature that all men feel a “rage for order” – the need to control his situation and bring unity to his existence. We all strive for order – we organize into families, into clubs, companies, societies, and nations so that we can be stronger.  “United we stand, divided we fall.”  This is called UNITY.

However, UNITY can become boring at times.  We need some VARIETY to avoid monotony.  This often leads to CONFLICT.  Biological psychological, and emotional needs trigger competition between individuals, and between parts of an individual.  Life is full of conflict, and it must be resolved, or it leads to the breakdown of the individual or the society. “A man cannot serve two masters.” But CONFLICT can be constructive — it leads to growth and maturity. Every story or play must have a conflict that leads to a solution; otherwise we lose interest in it.

DOMINANCE resolves the CONFLICT.  One of the opposing forces becomes stronger than the other and takes over the situation; or a decision is made that leads to a solution. DOMINANCE, or EMPHASIS, restores UNITY until the cycle is again broken.  In a play or story, the solution is often called the denouement.

Although these are the most important principles of design, there are two others that are also basic to nature:  BALANCE and RHYTHM.  BALANCE, or stability, is indispensable to human life. For every breath we inhale, we must exhale as well. Our days of work must be balanced by nights of rest. Disease is an upset of balance, either by germs or the action of our environment. Proper medication or living style will restore the balance. In nature the rough bark of a tree is balanced by the smoothness of its leaves, and sometimes the smallest flowers have the strongest fragrance, while bright, showy flowers have no noticeable scent. This too is BALANCE.

TO BE CONTINUED!