Inhaltsangabe1 Shape as Memory Storage 1.1 Introduction 1.2 New Foundations to Geometry 1.3 The World as Memory Storage 1.4 The Fundamental Laws 1.5 The Meaning of an Artwork 1.6 Tension 1.7 Tension in Curvature 1.8 Curvature Extrema 1.9 Symmetry in Complex Shape 1.10 Symmetry-Curvature Duality 1.11 Curvature Extrema and the Symmetry Principle 1.12 Curvature Extrema and the Asymmetry Principle 1.13 General Shapes 1.14 The Three Rules 1.15 Process Diagrams 1.16 Trying out the Rules 1.17 How the Rules Conform to the Procedure for Recovering the Past 1.18 Applying the Rules to Artworks 1.19 Case Studies 1.19.1 Picasso: Large Still-Life with a Pedestal Table 1.19.2 Raphael: Alba Madonna 1.19.3 Cézanne: Italian Girl Resting on Her Elbow 1.19.4 de Kooning: Black Painting 1.19.5 Henry Moore: Three Piece #3, Vertebrae 1.20 The Fundamental Laws of Art 2 Expressiveness of Line 2.1 Theory of Emotional Expression 2.2 Expressiveness of Line 2.3 The Four Types of Curvature Extrema 2.4 Historical Characteristics of Extrema 2.5 The Role of the Historical Characteristics 2.6 The Duality Operator 2.7 Picasso: Woman Ironing 3 The Evolution Laws 3.1 Introduction 3.2 Process Continuations 3.3 Continuation at M+ and m- 3.4 Continuation at m+ 3.5 Continuation at M- 3.6 Bifurcations 3.7 Bifurcation at M+ 3.8 Bifurcation at m- 3.9 The Bifurcation Format 3.10 Bifurcation at m+ 3.11 Bifurcation at M- 3.12 The Process-Grammar 3.13 The Duality Operator and the Process-Grammar 3.14 Holbein: Anne of Cleves 3.15 The Entire History 3.16 History on the Full Closed Shape 3.17 Gauguin: Vision after the Sermon 3.18 Memling: Portrait of a Man 3.19 Tension and Expression 4 SmoothnessBreaking 4.1 Introduction 4.2 The Smoothness-Breaking Operation 4.3 CuspFormation 4.4 Always the Asymmetry Principle 4.5 CuspFormation in Compressive Extrema 4.6 The Bent Cusp 4.7 Picasso: Demoiselles d'Avignon 4.8 The Meaning of Demoiselles d'Avignon 4.9 Balthus: Thérèse 4.10 Balthus: Thérèse Dreaming 4.11 Ingres: Princesse de Broglie 4.12 Modigliani: Jeanne Hébuterne 4.13 The Complete Set of Extrema-Based Rules 4.14 Final Comments

Michael Leyton's mathematical work on shape has been used by scientists in over 40 disciplines from chemical engineering to meteorology. His scientific contributions have received major prizes, such as a presidential award and a medal for scientific achievement. His new foundations to geometry are elaborated in his books in Springer-Verlag and MIT Press. Besides his scientific and mathematical work, he is also a highly exhibited painter and sculptor, and his architecture designs have been published by Birkhauser-Architectural. Also he is the composer of published string quartets. He is president of the International Society for Mathematical and Computational Aesthetics, and is on the faculty of the Psychology Department and the DIMACS Center for Discrete Mathematics and Theoretical Computer Science at Rutgers.