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

Abstract

This article investigates how curvature, commonly examined in differential geometry, functions as a conceptual and visual bridge between mathematics and the arts. Focusing on its presence in both abstract artworks (e.g., Kandinsky, Pollock) and architectural design (e.g., Gaudí), the study analyzes how mathematical curves such as parabolas, sinusoids, and exponential spirals are embedded in artistic compositions. Rather than treating curvature as a purely technical metric, the study presents it as a perceptual and compositional tool that structures form, evokes emotion, and communicates symbolic meaning. The paper introduces readers to core geometric principles underpinning curvature and their visual and compositional applications in art, aiming to make these concepts accessible to non-specialist readers. Employing case studies of historical and contemporary artworks, it highlights how mathematical patterns manifest intuitively in artistic practice. Key implications include the potential for curvature to foster interdisciplinary education, particularly through STEAM learning models that integrate science, technology, engineering, the arts, and mathematics. This approach encourages enriched classroom engagement, deeper visual literacy, and a broader appreciation of form as both analytic structure and expressive language.