Mathematical and Architectural Symmetry: A Comparative Analysis of Conceptualization

Symmetry is a shared concept in mathematics and architecture, yet its meaning and criteria of identification are not necessarily identical across the two fields. In contemporary mathematics, within the formulation adopted in this study, symmetry is characterized through the invariance of an object or structure under specified transformations. In architectural discourse, however, symmetry may appear as an observable geometric property, be reconstructed through mathematical analysis, participate in computational design generation, or be extended to broader discussions of perception, biological organization, environment, and meaning. This study asks: How does the conceptualization of symmetry differ between modern mathematics and architectural discourse? A comparative-conceptual review is employed to examine the mathematical formulation of symmetry and its different uses in architectural discourse. The comparison focuses on the object to which symmetry is attributed, the criteria used to identify it, the role of mathematical formulation, and the level at which the concept operates. The analysis shows that the difference cannot be reduced to a contrast between precise mathematical symmetry and visual architectural symmetry. Rather, architectural uses range from formal continuity with the transformation–invariance framework to analytical and generative applications, and in some cases to a broader conceptualization beyond explicit geometric criteria. The study therefore distinguishes conceptual continuity from conceptual identity and argues that the shared term symmetry does not necessarily imply identical conceptual criteria across disciplines. This distinction provides a more precise basis for interdisciplinary discussions of mathematical concepts in architecture without reducing either field to the conceptual framework of the other.

کلیدواژه ها:

Symmetry ، Mathematical Symmetry ، Architectural Symmetry ، Invariance ، Transformation