Includes bibliographical references (pages 395-401) and indexes

Space and geometry -- Motions on the plane -- The many symmetries of planar objects -- The many objects with planar symmetries -- Reflections on the mirror -- A raw material -- Stretching the plane -- Aural wallpaper -- The dawn of perspective -- A repertoire of drawing systems -- The vicissitudes of perspective -- The vicissitudes of geometry -- Symmetries in non-Euclidean geometries -- The shape of the universe -- Appendix: rule-driven creation

Most works of art, whether illustrative, musical or literary, are created subject to a set of constraints. In many (but not all) cases, these constraints have a mathematical nature, for example, the geometric transformations governing the canons of J.S. Bach, the various projection systems used in classical painting, the catalog of symmetries found in Islamic art, or the rules concerning poetic structure. This fascinating book describes geometric frameworks underlying this constraint-based creation. The author provides a development in geometry, a description of how these frameworks fit the creative process within several art practices, and discusses the perceptual effects derived from the presence of particular geometric characteristics