Optical Illusions in Rome: A Mathematical Travel Guide

Kirsti Andersen's Optical Illusions in Rome: A Mathematical Travel Guide is a book that any mathematician traveling to Rome and everyone leading a mathematical tour abroad that includes Rome will want to have on hand. She describes a number of places in Rome where mathematics has helped create the effects of trompe l'oeil two-dimensionally on walls or ceilings or even in three-dimensional settings. She also describes the mathematics behind Bernini's design of the oval at St. Peter's Square in Vatican City and the mathematics of various anamorphoses. I wish this book had been available at the time of the MAA's Mathematical Study Tour of Italy, where we saw a number of the sites she mentions, but without the benefit of this resource. 

 

The geometry of perspective of course is the critical mathematical topic for Andersen's discussions of trompe l'oeil and anamorphoses. The translator Viktor Blåsjö (the original of Andersen's work is in Danish) wrote an introductory essay providing a brief sketch of perspective in ancient Greece and Renaissance Italy. 

 

Andersen's intent in this short work is to provide "inspiration for travelers to Rome who are interested in mathematics, the history of mathematics, history, and art history ̶ including architecture." To that end, she provides very brief historical remarks on the artists, mathematicians, and religious orders that are relevant to the principal sites of Rome that she discusses. The sites include the Vatican, Villa Farnesina, Palazzo Spada, Chiesa di Sant'Ignazio, Trinità dei Monti, and Palazzo Massiano Terme. She offers a map showing the location of the five sites in Rome proper relative to the public transportation network; I would wish there was a second map of the sites on a standard tourist map of Rome. The first four chapters of the book discuss the optical illusions found at these sites.

 

Chapter 5 presents basic mathematical results about perspective, selected for their relevance to the discussions in Chapters 1-4 and includes a few exercises for the reader. Chapter 6 consists of exercises, at an advanced high school level, that are specific to the sites and material discussed in Chapters 1-5; one is to be carried out at a site, while another involves a YouTube search. No answers are provided to these exercises, so a teacher leading a tour and using the book will need to be prepared!

 

Color pictures or photographs on at least 35 pages enhance the book, with diagrams on additional pages as well. Over thirty references are provided to support the exposition; approximately half of these are readily available in English.

 

This book will certainly accompany me on my next trip to Rome, and if I were leading a student tour, I would find it indispensable. 

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Joel Haack (joel.haack@uni.edu) is a Professor of Mathematics at the University of Northern Iowa.