Exploring the Complementarity of Mathematical and Artistic Thinking in Design through 3-D Printing
DOI:
https://doi.org/10.18533/journal.v8i1.1577Keywords:
Art and Design, Mathematical Art, Steam, Technology in the Arts.Abstract
Most development of the “STEAM” (science, technology, engineering, arts, and mathematics) paradigm has been in the realm of education; however, the idea of combining technical and artistic thinking has many practical applications in product design. The more artistic side of technology design is often considered during design, but it tends to be subservient to the technical (“quantitative”) side due to the lack of a definite method for combining the technical and artistic concepts. New developments in 3-D printing and related technologies have opened some doors toward this by allowing the qualitative and quantitative design aspects to be expressed via a “common language” derived from the complementarity of mathematics and art. In this article, the complementarity of thought in design is discussed through the medium of 3-D printing. The basic concept of a “complementary design thinking” approach and work-flow of 3-D printing is explored in detail, with a focus on the value of the technology to bring together both the quantitative and qualitative approaches to design thinking. A case study using a 3-D printed model of the well-known Costa Minimal Surface from mathematics is presented and discussed to demonstrate the concepts. The concepts presented have clear policy implications for design, arts, education, engineering, and human-technology interaction research and practice; these implications are discussed in detail.
References
Andersson, S., Hyde, S.T., Larsson, K., & Lidin, S. (1988). Minimal surfaces and structures: From inorganic and metal crystals to cell membranes and biopolymers. Chemical Reviews, 88(1), 221-242. doi: 10.1021/cr00083a011
Boehm, B.W. (1988). A spiral model of software development and enhancement. Computer, 21(5), 61-72. doi: 10.1109/2.59.
Bownes, R. (2017). Minimalism, consumerism, and creativity. Retrieved from https://medium.com/@RobinBCreative/minimalism-consumerism-and-creativity-de171d4ac7cc on November 18, 2018.
Chadha, C., Crowe, K.A., Carmen, C.L., & Patterson, A.E. (2018). Exploring an AM-enabled combination-of-functions approach for modular product design. Designs, 2(4), 37. doi: 10.3390/designs2040037
Chong, Y.T., Chen, C-H., & Leong, K.F. (2009). A heuristic-based approach to conceptual design. Research in Engineering Design, 20(2), 97-116. doi: 10.1007/s00163-008-0059-9
Costa, C.J. (1984). Example of a complete minimal immersion in R^3 of genus one and three embedded ends. Bulletin Brazilian Mathematical Society, 15(1), 47-54. doi: 10.1007/BF02584707
Dorst, K. (2011). The core of ‘design thinking’ and its application. Design Studies, 32(6), 521-532. doi: 10.1016/j.destud.2011.07.006
Fields, J. (2018). Costa surface. Retrieved from https://www.thingiverse.com/thing:2882581 on August 21, 2018.
Gardner, H.E. (1994). Multiple intelligences: The theory in practice. New York, NY: Basic Books.
Goodwin, N., Nelson, J.A., Ackerman, F., & Weisskopf, T. (2008). Consumption and the consumer society. Retrieved from http://www.ase.tufts.edu/gdae/education_materials/modules/Consumption_and_the_Consumer_Society.pdf on December 1, 2018.
Gultekin, P. (2004). The negative effects of technology-driven product design on user-product interaction and product usability (M.S. thesis). Retrieved from http://etd.lib.metu.edu.tr/upload/12604954/index.pdf on December 12, 2018.
Henriksen, D. (2017). Creating STEAM with design thinking: Beyond STEM and arts integration. The STEAM Journal, 3(1), 11. doi: 10.5642/steam.20170301.11
Hodges, A.C. & Taylor, P.L. (2005). The business fallout from the rapid obsolescence and planned obsolescence of high-tech products: Downsizing of noncompetition agreements. The Columbia Science and Technology Law Review, 6, 1-31. url: http://www.stlr.org/cite.cgi?volume=6&article=3
Hyland, S. (2013, May). Technology’s negative impact on our culture. Retrieved from https://prezi.com/4bpp0vv_9txk/technologys-negative-impact-on-our-culture/ on December 12, 2018.
Melko, O.M. (2010). Visualizing minimal surfaces: Rendering solid models with the aid of 3D printers. The Mathematica Journal, 12, 1-18. url: https://www.mathematica-journal.com/2010/12/visualizing-minimal-surfaces/
Nylander, P. (2018). Minimal surfaces. http://bugman123.com/MinimalSurfaces/index.html. Accessed December 21, 2018.
Park, M. (2016). Defying obsolescence. In T. Cooper (Ed.), Longer Lasting Products: Alternatives to the Throwaway Society (pp. 77-106). London, UK: Routledge.
Ramey, K. (2012, November). Technology and society – Impact of technology on society. Retrieved from https://www.useoftechnology.com/technology-society-impact-technology-society/ on December 21, 2018
Saldana, J. (2015). Thinking Qualitatively: Methods of Mind. Thousand Oaks, CA: Sage Publications.
Segerman, H. (2016). Visualizing Mathematics with 3D Printing. Baltimore, MD: Johns Hopkins University Press.
Sen, S. (2004). Teaching quantitative thinking. Science, 304(5670), 518. doi: 10.1126/science.304.5670.518a
Stover, C. &Wesstein, E.W. (2018). Parametric equations (Wolfram-Alpha Online Resources). Retrieved from http://mathworld.wolfram.com/ParametricEquations.html on November 27, 2018.
Taylor, J.E. (1976). The structure of singularities in soap-bubble-like and soap-film-link minimal surfaces. Annals of Mathematics, 103, 489-539. doi: 10.2307/1970949
Traizet, M. (2008). On the genus of triply periodic minimal surfaces. Journal of Differential Geometry, 79, 243-275. doi: 10.4310/jdg/1211512641
Velimirovic, L.S., Radivojevic, G., Stankovic, M.S., &Kostic, D. (2008). Minimal surfaces for architectural constructions. Facta Universitatis: Architecture and Civil Engineering, 6(1), 89-96. doi: 10.2298/FUACE0801089V
Wesstein, E.W. (2018). Costa minimal surface (Wolfram-Alpha Online Resources). Retrieved from http://mathworld.wolfram.com/CostaMinimalSurface.html. Accessed December 21, 2018.
Wilson, S. (2002). Information Arts: Intersections of Art, Science, and Technology. Cambridge, MA: The MIT Press.
Withers, S.D. (2002). Quantitative methods: Bayesian inference, Bayesian thinking. Progress in Human Geography, 26(4), 553-556. doi: 10.1191/0309132502ph386pr
Younes, M.B. & Al-Zoubi, S. (2015). The impact of technologies on society: A review. IOSR Journal of Humanities and Social Science, 20(2), 82-86. doi: 10.9790/0837-20258286
Zeigler, B.P. & Muzy, A. (2016). Emergence at the fundamental system level: Existence conditions for iterative specifications. Systems, 4(4), 34. doi: 10.3390/systems4040034
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