He was a pupil at the
Art Students' League in
New York and of
William Merritt Chase, and a thorough student of classical art. He conceived the idea that the study of
arithmetic with the aid of
geometrical designs was the foundation of the proportion and symmetry in Greek architecture, sculpture and ceramics. Careful examination and measurements of classical buildings in
Greece, among them the
Parthenon, the
temple of Apollo at Bassæ, of
Zeus at
Olympia and
Athenæ at
Ægina, prompted him to formulate the theory of "dynamic symmetry" as demonstrated in his works
Dynamic Symmetry: The Greek Vase (1920) and
The Elements of Dynamic Symmetry (1926). It created a great deal of discussion. In 1921, articles critical of Hambidge's theories were published by Edwin M. Blake in
Art Bulletin, and by
Rhys Carpenter in
American Journal of Archaeology. Art historian Michael Quick says Blake and Carpenter "used different methods to expose the basic fallacy of Hambidge's use of his system on Greek art—that in its more complicated constructions, the system could describe any shape at all." In 1979 Lee Malone said Hambidge's theories were discredited, but that they had appealed to many American artists in the early 20th century because "he was teaching precisely the things that certain artists wanted to hear, especially those who had blazed so brief a trail in observing the American scene and now found themselves displaced by the force of contemporary European trends."
Dynamic symmetry Dynamic
symmetry is a proportioning system and natural design methodology described in Hambidge's books. The system uses
dynamic rectangles, including
root rectangles based on ratios such as , , , the
golden ratio (φ = 1.618...), its square root ( = 1.272...), and its square (φ2 = 2.618....), and the
silver ratio (\delta_s=2.414...). From the study of
phyllotaxis and the related
Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...), Hambidge says that "a much closer representation would be obtained by a substitute series such as 118, 191, 309, 500, 809, 1309, 2118, 3427, 5545, 8972, 14517, etc. One term of this series divided into the other equals 1.6180, which is the ratio needed to explain the plant design system." This substitute sequence is a
generalization of the Fibonacci sequence that chooses 118 and 191 as the beginning numbers to generate the rest. In fact, the standard Fibonacci sequence provides the best possible rational approximations to the golden ratio for numbers of a given size. A number of notable American and Canadian artists have used dynamic symmetry in their painting, including
George Bellows (1882–1925),
Maxfield Parrish (1870–1966), The
New Yorker cartoonist
Helen Hokinson (1893–1949), Al Nestler (1900–1971),
Kathleen Munn (1887–1974), the children's book illustrator and author
Robert McCloskey (1914–2003), and Clay Wagstaff (b. 1964).
Elizabeth Whiteley has used dynamic symmetry for works on paper. == Applications ==