# Blog Archives

## COMPOSING WITH FIBONACCI NUMBERS

Now, how can you use the Fibonacci numbers to make a composition that conforms to the Golden Mean or Golden Section? If you use the correct size for the overall composition, it would be about 10 x 16″ – (1-1.618) – a larger format would be 13 x 21″. In order to break this apart, and position your center of interest in the correct spot, you will need to plot the numbers on a sheet of graph paper the correct size. For instance, using a format 13 x 21″, I measured off a 13 x 13″ square on one side, which left a rectangle of 8 x 13″. From this, I formed an 8 x 8″ square leaving a 5 x 8″ rectangle. Then I measured inside this rectangle a square that is 5 x 5″ leaving a rectangle of 3 x 5″. Inside this rectangle, I formed a 3 x 3″ square, leaving a rectangle of 2 x 3″. Inside this rectangle I measured a 2 x 2″ square, leaving a rectangle of 1 x 2″. This rectangle was divided into two squares 1 x 1″ each. So you see, the sequence from inside out is 1,1,2,3,5,8,13,21 — the Fibonacci number sequence. Here’s my result–

If you draw a spiral connecting the corners of each square, it looks like the kind of spirals you see in shells, pine cones, flowers, etc. How about that!

The center of interest should be placed in the smallest squares — the largest section should conform to the principle of using the same value with different hues to keep it integrated. Here is a collage I made using this type of composition. It is a poem collage which reads from the inside out: The earth turns round. Faces the sun; A new day is born. Shall I change another’s life today? Shall I reach a goal or realize my life’s mission? Or shall I still live one day at a time, in the hope that the path I follow is His?

I invite you to try a composition in this format and see how you like it!

## THE GOLDEN MEAN: PERFECT PROPORTION

A discussion by Steven Sheehan in the *American Artist Magazine*, September 2007, included this definition of the Golden Mean or Golden Section: “Also known as the Golden Mean, the Golden Section is a canon of proportion used in painting, sculpture, and architecture thought to have special meaning because of its correspondence to the principles of the universe.” This proportion is thought to be most pleasing to the human eye, and can be used in designing visual art compositions.

In the 1930’s, Pratt Institute in New York interviewed several hundred of its art students as to which vertical frame they liked the best and the least. The ratio of 1:2 was the least liked, while the 1:618 ratio was the preferred frame. If this ratio was to be used in a compositional format, the shape of your paper or canvas should be 10 x 16″ rather than 11 x 14″ or 12 x 16″ (standard sizes). To figure out a larger format using the golden mean start with a square. Using a compass, place the center pin at the midpoint of the bottom edge (B). Swing an arc out from an upper corner and extend the bottom edge of the square out to meet the arc (segment C). Complete the rectangle with B=C as the base. Now A (height) is in the same proportion of B+C as B+C is of A+B+C (the Golden Mean).

We all know how to find the “sweet spot” in a composition for the center of interest: divide the format into thirds both horizontally and vertically, and where any of the sections cross is a good place to put your center of interest. This is the easy way, but not quite in the same proportions as the Golden Mean. *The Pastel Journal* of December 2005 features an artist who uses the Golden Section for her compositions: Sydney McGinley. Not only does she use the ratio as her format and for placing shapes within the composition, but to choose the right proportion of hues.

Here is an illustration of how to devise your own format in the Golden Section using the method outlined above:

## OUT YOUR WINDOW

LOOK OUT A WINDOW IN YOUR HOUSE/APARTMENT. USING THE WINDOW FRAME AS YOUR FORMAT, MAKE ANOTHER FORMAT IN YOUR SKETCHBOOK CORRESPONDING TO THE SHAPE OF THE WINDOW. THINK OF THE PANE OF GLASS AS THE PICTURE PLANE AND DRAW WHAT YOU SEE FROM THAT VIEWPOINT. THIS DRAWING WAS DONE FROM ONE OF THE WINDOWS IN MY UPSTAIRS STUDIO.