Exploring the Cardioid: Between Circles and Symmetry

Abstract

This article aims to explore theoretical and applied aspects of Differential Geometry through the study of the cardioid curve. Initially, a theoretical foundation is presented on fundamental concepts such as regularity and curvature. Next, the cardioid is introduced as a significant example of a plane curve, whose symmetry, parameterization, and curvature are analyzed in light of Differential Geometry. The methodology adopted is based on a literature review, focusing on identifying the analytical tools used in previous research and on a deeper theoretical understanding of the topic. Applications of the cardioid in areas such as acoustics, optics, and plant morphology are also discussed, highlighting its interdisciplinary nature. The results confirm the relevance of the cardioid both for the development of mathematical skills in the context of Differential Geometry and for its practical applicability in different fields of knowledge.