The original idea of the book whose main theme is Visible harmonies, was to accompany an exhibition with the same title that was planned to take place in 2013 at the MART (Contemporary and Modern Art Museum of Trento and Rovereto) as it was announced in the previous volume of the Imagine Math series. However, due to budget cuts, it had to be cancelled at the last minute.
The idea is the same as in the two previous volumes. Editor Michele Emmer brought together papers by mathematicians and artists alike which discuss the close relationship that sometimes exists between mathematics and art.
The 23 papers are grouped into 8 parts. Eight of the papers constitute the first and most general part on Mathematics and art. There is a short discussion of an exhibition at the Institut des Hautes Études near Paris in the period October 2011 - March 2012. But there are several other, often geometry-related, mathematical subjects that are placed in an historical perspective. For example there is a paper about the extension of the classical Platonic solids by more general and complex polyhedra of Kepler. Another historical period is Classicism, introducing symmetry in architecture, and much later the come-back of geometry to the forestage of mathematics when new geometries arose after leaving Euclid's parallel postulate. The representation of space-time became important in cubism, and it plays an important role in many science fiction stories. Since the middle of the 20th century we also find abstract art that is based on abstract concepts (e.g. Sol LeWitt, Donald Judd). In their paper, the artists E. Fiorelli, C. Di Rienzo, and M. Cappellani present their performance project In-tensioni reciproche (videos can be found on the web) in which abstract concepts like tension and elasticity are given shape with elastic strings, light, dance, and photography.
Part two A tribute to Mandelbrot consists of two papers that introduce the properties of fractals, and the concept of fractal dimension, omnipresent in nature but also applied in different works on the edge of mathematics and art. Two papers in the part on mathematics, Architecture and Design start from topology that can continuously transform a surface without changing its topological properties. This is linked to 'fluid architecture' in which smooth curves are essential. These smooth curves can also be used to design smooth surfaces that generate 'Pasta by Design', i.e., new shapes of pasta with optimal consumer properties but that also have a pleasant form. The third paper is again about architecture telling the history of the church San Geminiano in the Piazza San Marco in Venice.
Three other papers deal with Mathematics and literature. A mathematical model describes the passion and tension in the relation of a couple of lovers which is checked with classical examples from literature. Matilde Marcolli introduces the reader to her mathematical themes in the stories and collages she used in her Tales for the Wolf (1993) and how this is in contrast with her more recent view as a professional mathematician using graffiti lyrics in her book Street Science (2013). Finally, there are poems and sketches by Claudio Zanini originally inspired by the Black Square painting of Vladimir Malevich.
In the part on Mathematics and applications, the discussion is again more mathematical. Fractals are back with iterated function systems plotting basins of attractions for roots of polynomials, resulting in the familiar pretty fractal pictures. Social consequences can be dramatic when judicial errors are the result of conclusions drawn from intuitively conceived probabilities which are shown wrong by correct statistical analysis. More statistics in practical situations need careful attention when the bell shaped normal distribution is not the model of choice, but exponential like distributions are more appropriate. Partial differential equations can be used to solve the so called shape from shading problem. The problem is to reconstruct a three-dimensional view of two-dimensional images taken with different light sources.
As usual in the books edited by M. Emmer, we also find mathematics interference with cinema and theater, and also Venice often plays a role. That are the subjects of the remaining parts. The film paper is about the way cinema manipulates space-time by all kind of editing tricks: fast forward, flash back, slow motion, split screen,... The theater paper describes a software project eMotions that should transform information about objects into a script for animated situations, which may result in a show, an installation or just images. Venice was already discussed in the paper about the church San Geminiano, but the last chapter is about an ancient woodcut by Jacopo de' Barbari representing a perspective plan of Venice. The plan is so detailed that a lot can be learned from over 600 ships, boats, vessels, and port and shipyard related items that are depicted.
The overall emphasis of the book is obviously on the interaction between mathematics and art. Some papers are written by mathematicians, others by artists. Hence some are more mathematical, others are more philosophical or just descriptively reporting. There are some formulas, but this is certainly not the place where you would look for the mathematical details of a method. As Emmer describes in his introduction, the presence and influence of mathematics on all kind of art forms, is growing and expositions with a strong mathematical component gain general interest. Readers who know some of the books in the series that Michele Emmer has edited before. will find here more papers in the same scope. Those who don't know his previous books, and have an open mind, will love this and may be interested in retroactively read the previous books as well.