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Dynamic symmetry: a history and analysis. (English) Zbl 1472.00050

Summary: We discuss a number of the mathematical ideas behind Dynamic Symmetry, an approach to design championed by Jay Hambidge and popular in the 1920s and 1930s. We discuss Hambidge’s interest in the geometry of root rectangles and the golden ratio, and how Dynamic Symmetry influenced a generation of artists and art and mathematics educators.

MSC:

00A66 Mathematics and visual arts
01A60 History of mathematics in the 20th century
Full Text: DOI

References:

[1] Ahern L. (1939). Art in geometry. The Mathematic Teacher, 32(4), 156-162. · doi:10.5951/MT.32.4.0156
[2] Bennett A. A. (1922). Dynamic symmetry, the Greek vase by Jay Hambidge. The American Mathematical Monthly, 29(4), 164-170. https://doi.org/10.2307/2298893
[3] Blake E. (1921). Dynamic symmetry: A criticism. The Art Bulletin, \(3(3), 107-127\). https://doi.org/10.2307/3046381 · doi:10.2307/3046381
[4] Bouleau C. (1963). The painter’s secret geometry: A study of composition in art. Harcourt, Brace & World, Inc.
[5] Carpenter R. (1921). Dynamic symmetry: A criticism. American Journal of Archaeology, 25(1), 18-36. https://doi.org/10.2307/497887 · doi:10.2307/497887
[6] Caskey L. D. (1919). Department of classical art. In Annual report for the year: Museum of fine arts, Boston (Vol. 44, pp. 101-102). Museum of Fine Arts.
[7] Church A. H. (1904). On the relation of phyllotaxis to mechanical law. William & Norgate. · doi:10.5962/bhl.title.57125
[8] Conway R. (2007). The powerful hand of George Bellows. Trust for Museum Exhibitions.
[9] D’Arcy T. (1892). On growth and form. Cambridge University Press.
[10] Devlin K. (2020). The Myth that will not go away. https://www.maa.org/external/archive/devlin/devlin_05_07.html
[11] Eckholm A. (1939). General mathematics for art teachers. The Mathematic Teacher, 32(8), 365-367.
[12] Edwards E. B. (1932). Dynamarhythmic design: A book of structural pattern. The Century Company. Reprinted (1967) as Pattern and Design with Dynamic Symmetry: How to create art deco geometrical designs. Dover Publications.
[13] Fischler R. (1981). On the application of the golden ratio in the visual arts. Leonardo, 14(1), 31-32. https://doi.org/10.2307/1574475 · doi:10.2307/1574475
[14] Frame J. S. (1942). Clubs and allied activities. The American Mathematical Monthly, 49(10), 679-682. https://doi.org/10.1080/00029890.1942.11991306
[15] Ghyka M. (1946). The geometry of art and life. Sheed and Ward, Inc. · Zbl 0451.51013
[16] Griffin R. C. (2013). George Bellows: Washington, New York and London. The Burlington Magazine, 155(1322: Art in France), 342-344.
[17] Gugle M. (1926). Recreational values achieved through mathematics clubs in secondary schools. The Mathematics Teacher, 19(4), 214-218. · doi:10.5951/MT.19.4.0214
[18] Gugle M. (1928). Dynamic symmetry. In National council of teachers of mathematics 3rd year book (pp. 57-64). National Council of Teachers of Mathematics.
[19] Hambidge J. (1926). The elements of dynamic symmetry. Brentano’s Inc.
[20] Hambidge J. (1932). Practical applications of dynamic symmetry. Yale University Press.
[21] Heath T. L. (Trans.). (1956). Euclid’s elements. Dover.
[22] Huntley H. E. (1970). The divine proportion: A study in mathematical beauty. Dover Publications. · Zbl 0221.00007
[23] Hurlburt L. (1937). The Mexican muralists in the United States. University of New Mexico Press.
[24] Jaffee B. (2005). Before the New Bauhaus: From industrial drawing to art and design education in Chicago. Design Issues, 21(1), 41-62. https://doi.org/10.1162/0747936053103066 · doi:10.1162/0747936053103066
[25] Kappraff J. (1990). Connections: The geometric bridge between art and science. McGraw-Hill.
[26] Mansfeld R. (1951). Mathematics for prospective teachers in elementary schools. The American Mathematical Monthly, 48(4), 248-250. https://doi.org/10.2307/2302720 · doi:10.2307/2302720
[27] Markowsky G. (1992). Misconceptions about the Golden Ratio. The College Mathematics Journal, 23(1), 2-19. https://doi.org/10.1080/07468342.1992.11973428 · Zbl 07917122
[28] McWhinnie H. J. (1986). A review of the use of dynamic symmetry, the golden section and dynamic symmetry in contemporary art. Leonardo, 19(3), 241-245. https://doi.org/10.2307/1578244 · doi:10.2307/1578244
[29] Miliotes D. (2002). The murals at the new school for social research. In R. G. Mello and D. Miliotes (Eds.), Jose Clemente Orozco in the United States (pp. 118-141). W. W. Norton & Company.
[30] Mosely H. (1938). On the geometrical forms of turbinated and discoid shells. Philosophical Transactions of the Royal Society of London, \(4, 351-370\).
[31] Neumeyer A. (1951). Orozco’s mission. College Art Journal, 10(2), 121-130. https://doi.org/10.2307/772309 · doi:10.2307/772309
[32] Ollmann L. F. (1950). Clubs and allied activities. The American Mathematical Monthly, 57(3), 197-200. https://doi.org/10.1080/00029890.1950.11999515
[33] Orozco J. C. (1962). An autobiography. The Texas Pan-American Series.
[34] Quick M. (1992). Technique and theory: The evolution of George Bellows’s painting style. In M. Quick, J. Myers, M. Doezema & F. Kelly (Eds.), The paintings of George Bellows (pp. 9-95). Amon Carter Museum.
[35] Richmond V. A. (1927). A number of things for beginners in geometry. The Mathematics Teacher, 20(3), 142-149. · doi:10.5951/MT.20.3.0142
[36] Richter G. M. A. (1922). Dynamic symmetry from the designer’s point of view. American Journal of Archaeology, 26(1), 59-73. https://doi.org/10.2307/497635 · doi:10.2307/497635
[37] Ross D. (1907). A theory of pure design: Harmony, balance, rhythm. Houghton-Mifflin.
[38] Schaff W. (1950). Mathematics and art. The Mathematics Teacher, 43(8), 423-426. · doi:10.5951/MT.43.8.0423
[39] Schaff W. (1951). Art and mathematics: A brief guide to source materials. The American Mathematical Monthly, 58(3), 167-177. https://doi.org/10.1080/00029890.1951.11999651 · Zbl 0042.38901
[40] Smith D. E. (1921). Religio mathematici. The Mathematics Teacher, 14(8), 413-426. · doi:10.5951/MT.14.8.0413
[41] Stephen M. (1956). The mysterious number phi. The Mathematics Teacher, 49(3), 200-204. · doi:10.5951/MT.49.3.0200
[42] Weir B. L. (1930). Relating art and mathematics. The Mathematics Teacher, 23(1), 60. · JFM 56.0840.10 · doi:10.5951/MT.23.1.0060
[43] Whiteley E. (2008). A process for generating 2D paintings and drawings from geometric diagrams. Journal of Mathematics and the Arts, \(2(1), 29-38\). https://doi.org/10.1080/17513470802014356 · Zbl 1153.51008
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