Geometric Exploration of Facial Symmetry

This GeoGebra example demonstrates and quantifies the geometric asymmetry of the human face using mathematical transformations. The core mathematical concepts include reflectional symmetry, axial symmetry, translation, and vector geometry. To construct the model, the tool utilizes commands such as Line, Translate, and Mirror, operating on geometric objects including points A, B, C, D, E, F, vectors v and u, and imported images pic1 and pic2. By applying these transformations, it generates mirrored and translated versions (pic1', pic2', etc.) to visually and quantitatively analyze facial asymmetry. This interactive applet is highly suitable for high school or introductory college geometry courses, transformation geometry lessons, and mathematical modeling of biological symmetry.