Ebook: Imagine math: Between culture and mathematics

Imagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. This book is intended to contribute to grasping how much that is interesting and new is happening in the relationships between mathematics, imagination and culture. With a look at the past, at figures and events, that help to understand the phenomena of today. It is no coincidence that this volume contains an homage to the great Italian artist of the 1700s, Andrea Pozzo, and his perspective views. Theatre, art and architecture are the topics of choice, along with music, literature and cinema. No less important are applications of mathematics to medicine and economics. The treatment is rigorous but captivating, detailed but full of evocations, an all-embracing look at the world of mathematics and culture

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Euclid and His Modern Rivals is a deeply convincing testament to the Greek mathematician's teachings of elementary geometry. Published in 1879, it is humorously constructed and written by Charles Dodgson (better known outside the mathematical world as Lewis Carroll, the author of Alice in Wonderland) in the form of an intentionally unscientific dramatic comedy. Dodgson, mathematical lecturer at Christ Church, Oxford, sets out to provide evidentiary support for the claim that The Manual of Euclid is essentially the defining and exclusive textbook to be used for teaching elementary geometry. Euclid's sequence and numbering of propositions and his treatment of parallels, states Dodgson, make convincing arguments that the Greek scholar's text stands alone in the field of mathematics. The author pointedly recognises the abundance of significant work in the field, but maintains that none of the subsequent manuals can effectively serve as substitutes to Euclid's early teachings of elementary geometry Part 1. Introduction -- Introduction / Michele Emmer -- Part 2. Homage to Benoît Mandelbrot -- The Fantastic World of Tor' Bled-Nam / Michele Emmer -- Part 3. Venice and "La Fenice" -- The Reconstruction of the Teatro La Fenice: "Splendidezze" and "dorature" (Gleam and Gilding) / Elisabetta Fabbri -- Part 4. Homage to Andrea Pozzo -- Exactitude and Extravagance: Andrea Pozzo's "Viewpoint" / Filippo Camerota -- The Apse Scenes in the Prospective Inventions of Andrea Pozzo / Silvia Carandini -- Andrea Pozzo: Art, Culture and Mathematics / Marco Costamagna -- Part 5. Homage to Hypatia -- Hypatia as Polymath / Michael A. B. Deakin -- Women's Contributions to the Progress of Mathematics: Lights and Shadows / Elisabetta Strickland -- Hypatia's Dream / Massimo Vincenzi -- Part 6. Mathematics and Art -- Modern Geometry versus Modern Architecture / Isabeau Birindelli and Renata Cedrone -- Visual Harmonies: An Exhibition on Art and Math / Michele Emmer -- Emilio Prini, Alison Knowles, and Art's Logic / Cornelia Lauf -- All the Numbers End in Numbers. On a Work by Alighiero Boetti / Andrea Valle -- Part 7. Mathematics and Literature -- The Unreasonable Effectiveness of Mathematics in Human Sciences: The Attribution of Texts to Antonio Gramsci / Dario Benedetto, Emanuele Caglioti and Mirko Degli Esposti -- Lost in a Good Book: Jorge Borges' Inescapable Labyrinth / William Goldbloom Bloch -- Part 8. Mathematics and Applications -- The Many Faces of Lorenz Knots / Marco Abate -- Waiting for ABRACADABRA. Occurrences of Words and Leading Numbers / Emilio De Santis and Fabio Spizzichino -- Aperiodic Tiling / Gian Marco Todesco -- Part 9. Mathematics and Medicine -- Connecting Ventricular Assist Devices to the Aorta: A Numerical Model / Jean Bonnemain, Simone Deparis and Alfio Quarteroni -- Part 10. Mathematics Elsewhere -- Numeracy, Metrology and Mathematics in Mesopotamia: Social and Cultural Practices / Grégory Chambon -- Origami and Partial Differential Equations / Paolo Marcellini and Emanuele Paolini -- Part 11. Mathematics and Film -- The Möbius Strip / A film by Edouard Blondeau / Edouard Blondeau -- From Brigitte Bardot to Angelina Jolie / Michele Emmer -- Part 12. Homage to Luca Pacioli -- The Mathematical Ideas of Luca Pacioli Depicted by Iacopo de' Barbari in the Doppio ritratto / Enrico Gamba -- De divina proportione: From a Renaissance Treatise to a Multimedia Work for Theatre / Simone Sorini -- Part 13. Mathematics and Music -- Towards a Rational Practice of Arithmetic. A Model for Musical (and Multimedia) Composition / Francesco Scagliola