Conceptual Formation of Curvature in the Logic of Art: An Educational Mathematical Approach

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.