Conceptual Formation of Curvature in the Logic of Art: An Educational Mathematical Approach
Keywords:
Curvature, Art, Differential Geometry, Aesthetic, STEAM education
Abstract
This paper explores the conceptual formation of curvature as a unifying principle between mathematical reasoning and artistic expression. Curvature, traditionally studied within the field of differential geometry, finds a compelling counterpart in the visual language of art, manifesting in forms, lines, and symbolic representations across various artistic traditions. This interdisciplinary approach introduces readers, particularly non-specialists, to the foundational mathematical concepts underlying curvature, highlighting their intuitive and interpretive applications in visual art. By examining parabolic, sinusoidal, and exponential curves within both abstract and figurative compositions, the study bridges the epistemological gap between the analytic and the aesthetic. In doing so, it contributes to contemporary discourse in both educational and creative domains. The paper also underscores the educational value of this cross-disciplinary methodology, emphasizing its potential to enrich classroom instruction, enhance visual literacy, and support STEAM-based learning initiatives.
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References
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2. Arnheim, R. (1974). Art and Visual Perception: A Psychology of the Creative Eye. University of California Press.
3. Boaler, J. (2016). Mathematical mindsets: Unleashing students' potential through creative math, inspiring messages, and innovative teaching. Jossey-Bass/Wiley.
4. Devlin, K. (2011). Mathematics education for a new era: Video games as a medium for learning. 1st Edition, A K Peters/CRC Press. https://doi.org/10.1201/b10816
5. Fierro-Newton, P. (2024). The Emotional Impact of Curved vs. Angular Designs. https://neurotectura.com/2024/12/31/the-emotional-impact-of-curved-vs-angular-designs/?utm_source=chatgpt.com
6. Friedman, M. & Carter, M. (1991). Curvature in Art and Nature. Journal of Aesthetic Education, 25(3), 85-96.
7. Gao, J. and Newberry, M. (2024). Fractal Scaling and the Aesthetics of Trees, Physics and Society, arXiv:2402.13520 [physics.soc-ph]. https://doi.org/10.48550/arXiv.2402.13520
8. Gombrich, E. H. (1960). Art and Illusion: A Study in the Psychology of Pictorial Representation. Princeton University Press.
9. Grieve, A. (2018). The Scientific Narrative of Leonardo’s Last Supper, Jour. of Excellence in Integrated Writing at Wright State University, Vol. 5(1).
10. Henderson, D. W. & Taimina, D. (2001). Crocheting the hyperbolic plane. The Mathematical Intelligencer 23, 17–28. https://doi.org/10.1007/BF03026623
11. Henriksen, D., Mishra, P. & Fisser, P. (2016). Infusing creativity and technology in 21st-century education: A systemic view for change. Educational Technology & Society, 19(3), 27–37. https://www.researchgate.net/publication/311670214
12. Hoffman, D. D. & Richards, W. (1984). Parts of recognition. Cognition, 18(1-3), 65-96. https://doi.org/10.1016/0010-0277(84)90022-2
13. Kandinsky, W. (1947). Concerning the Spiritual in Art. Wittenborn, Schultz, Inc.
14. Kempkes, S. N., Slot, M. R., Freeney, S. E., Zevenhuizen, S. J. M., Vanmaekelbergh, D., Swart, I., & Morais Smith, C. (2019). Design and characterization of electrons in a fractal geometry. Nat. Phys. 15, 127–131. https://doi.org/10.1038/s41567-018-0328-0
15. Kreyszig, E. (1991). Differential Geometry. Dover Publications.
16. Kühnel, W. (2006). Differential Geometry: Curves, Surfaces, Manifolds. American Mathematical Society. ISBN 0-8218-3988-8.
17. Livio, M. (2002). The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. Broadway Books.
18. McRobie, A. (2017). The Seduction of Curves: The Lines of Beauty that Connect Mathematics, Art and the Nude. Princeton University Press. ISBN: 9780691175331.
19. Middleton, J. & Petruzzello, M. (2024). "Sagrada Família". Encyclopedia Britannica, 3 Oct. 2024, https://www.britannica.com/topic/Sagrada-Familia
20. Pressley, A. (2001). Elementary Differential Geometry. Springer.
21. Rose, D. H., & Meyer, A. (2002). Teaching every student in the digital age: Universal design for learning. Association for Supervision and Curriculum Development (ASCD). ISBN: ISBN-0-87120-599-8.
22. Ruta, N., Vano, J., Peppereli, R., Corradi, G. B., Chuquichambi, E. G., Rey, C. & Munar, E. (2023). Preference for paintings is also affected by curvature. Psychology of Aesthetics, Creativity, and the Arts, 17(3), 307-321. https://doi.org/10.1037/aca0000395
23. Silva, P. J. & Barona, C. M. (2009). Do People Prefer Curved Objects? Angularity, Expertise, and Aesthetic Preference, Empirical Studies of Arts, 27(1), 25-42. https://doi:10.2190/EM.27.1.b
24. Sinclair, N., & Watson, A. (2001). The aesthetic is relevant. For the Learning of Mathematics, 21(1), 25–32. https://eric.ed.gov/?id=EJ627148
25. Smith, D. E. (1958). History of Mathematics, Vol. 2. New York, NY: Dover Publications.
26. Sousa, D. A. (2016). How the brain learns (5th ed.). Corwin Press. https://www.amazon.com/How-Brain-Learns-David-Sousa/dp/1506346308
27. Taylor, R. P., Spehar, B., Clifford, C. W. G., & Newell, B. R. (2008). The Visual Complexity of Pollock’s Dripped Fractals. In: Minai, A.A., Bar-Yam, Y. (eds.) Unifying Themes in Complex Systems IV, 175–182. Springer, Heidelberg.
28. Taylor, R. P., Spehar, B., Van Donkelaar, P., & Hagerhall, C. M. (2011). Perceptual and physiological responses to Jackson Pollock’s fractals. Frontiers in Human Neuroscience, Vol. 5, Article 60, 1-13. doi:10.3389/fnhum.2011.00060
29. UNESCO. (2015). Cracking the code: Girls' and women's education in science, technology, engineering and mathematics (STEM). United Nations Educational, Scientific and Cultural Organization. https://unesdoc.unesco.org/ark:/48223/pf0000253479
Published
2025-06-16
How to Cite
Petrakis, V., Seremeti, L., & Kougias, I. (2025). Conceptual Formation of Curvature in the Logic of Art: An Educational Mathematical Approach. European Scientific Journal, ESJ, 42, 215. Retrieved from https://eujournal.org/index.php/esj/article/view/19640
Section
ESI Preprints
Copyright (c) 2025 Vassileios Petrakis, Lambrini Seremeti, Ioannis Kougias
This work is licensed under a Creative Commons Attribution 4.0 International License.
