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1. Tilings of the plane and the sphere. Platonic solids. Visualization of the notions of symmetry, curvature and dimension through works by Escher, van Gogh, Buckminster Fuller, Italo Calvino and Lewis Carrol. Symmetry in Chemistry: the intervention of mathematics in the discovery of the molecule with 60 carbon atoms.

2. The third and fourth dimensions: analysis of this concept in the works of Picasso, Escher and Dalí.

3. The isoperimetric problem. Discussion about the narrative Flatland, by E. Abbott. Properties that characterize or not the circles, and their use in paintings of Amadeo de Souza-Cardoso and in Sports Sciences. Constant-width curves and superelipses of Piet Hein in urban architecture.

4. Construction of maps. Central, Archimedean, Mercator and stereographic projections. Importance of the properties of these functions in various works of classical architecture and modern sculpture. The non-Euclidean distances and the role of axioms in Mathematics. Infinity in the perception of reality: comments about O livro de areia, by Jorge Luis Borges.

5. The art made by computers. Iteration of functions. Newton's method and a problem in Physics concerning nuclear residues. Fractals. The comic strip as a privileged means of promoting mathematics. Details of fractal nature in Pollock's paintings and in the structure of some narratives by James Joyce. The golden ratio and Fibonacci sequence: artistic manifestations of rational approximations of this number in Mondrian's work.

6. The mathematical origin of the pacemaker. Jordan Curve Theorem intervention in the work of the artist Fiona Ross.

7. Use of encryption methods in Edgar Allan Poe's The Golden Bug. Modular arithmetic, the vocabulary in George Perec's La disparition, and the alphabet (color and form) in Miró's surrealist work. The enigmas in Albrecht Durer's etchings.

8. Dating art using the radioactive decay of some atoms. Examples of forgeries of famous paintings by Vermeer, Modigliani and Andrea Mantegna.

9. Algebra in musical composition.

10. A few dialogues of the book Godel, Escher, Bach: An eternal golden braid, of Douglas Hofstadter. Discussion about what is true and what is provable in Mathematics: the contributions in this context of Poincaré, Proust, Magritte and Escher. The paradox of Bertand-Russel in O aleph, by Jorge Luis Borges.

11. Geometric constructions with rule and compass, or with origami.

12. Isometrics of the plane. Group of symmetries of a flat figure: digital visit to the Alhambra Palace. Linear and rider perspective. Essays of Brunelleschi, Masaccio, Piero della Francesca, Alberti, Pélerin and Monge. Anamorphoses. Impact of the use of perspective on works by Tintoretto, Leonardo da Vinci, Michelangelo, Holbein the Younger and William Hogarth.