This journal issue proposes reflections on the central role of geometry within the science of representation, tracing its cultural and disciplinary developments from the Florentine school to contemporary debates. Particular attention is given to perceptive geometry and homology, explored as tools for interpreting distortion, transformation, spatial continuity, and the renewed dialogue between theory and practice. References to past and present research underline the importance of opening geometry to wider academic exchange, integrating historical depth with technological innovation. The volume reflects on geometry as a space where passion and rationality converge in pursuing beauty, form, and knowledge, reaffirming its role as the enduring core of representation.