Fig. 1. Photograph of “Silence,” 1929, with dynamic symmetry lines drawn over it by Bisttram | Fig. 2. Golden section rectangle divided into proportional areas. |
The lines that Bisttram drew over this photograph of his drawing “Silence” demonstrate that he constructed the drawing using the golden section rectangle. This is an example of Bisttram’s use of dynamic symmetry, a system of picture construction developed by Jay Hambidge in the early 20th century. Bisttram used dynamic symmetry in all of his compositions and taught it in all of his classes.
The golden section rectangle is often described as a 1.618+ rectangle. This can be seen in Fig. 2 as follows: If line cd =1, then line bd=1.618+.
In Fig. 2, notice that efcd is a square, as is abgh. Also notice that smaller golden section rectangles are nested inside the larger golden section rectangle abcd: abef and ghcd are golden section rectangles. Therefore, any golden section rectangle can be divided into a square and a smaller golden section rectangle on its side.
Additionally, in Fig. 2 efgh is made up of a square and a golden section rectangle. Other golden section rectangles are made with the lines ij and kl, so that gscj is another golden section rectangle.
The lines mn and op cut the rectangle at the “eyes,” one of which is marked in fig. 2 at t. The eyes are the point around which the golden section rectangles whirl, which refers to the fact that when a golden section rectangle is reduced into its components – a square and a smaller golden section rectangle – the smaller golden section rectangle is on its side. This reduction, when repeated successively, forms the logarithmic spiral, which is shown in Fig. 4.
This spiral is found in many forms of nature; for this reason, Bisttram and others who dynamic symmetry felt that they were embedding the life force into their drawings when they used the golden section rectangle. Jay Hambidge called it a whirling square rectangle.
Fig. 3 shows how to construct a golden section rectangle. Draw a square abcd. Mark “e” at the midpoint of a side of the rectangle. Using a compass, place the point of the compass at e and the pencil end of the compass at b, and then drop an arc to f. Then draw the golden section rectangle adgf. Again, note that gfbc is a smaller golden section rectangle on its side.
Fig. 3. How to construct a golden section rectangle. | Fig. 4. The logarithmic spiral embedded in the golden section rectangle. |