The Geometry of an Art: The History of the Mathematical Theory of Perspective from Alberti to Monge is a book in the history of mathematics, on the mathematics of graphical perspective. It was written by Kirsti Andersen, and published in 2007 by Springer-Verlag in their book series Sources and Studies in the History of Mathematics and Physical Sciences.
This book covers a wide span of mathematical history, from 1435 to 1800, and a wide field of "around 250 publications by more than 200 authors".After three introductory chapters on the beginnings of perspective with the works of Leon Battista Alberti, Piero della Francesca, Leonardo da Vinci, and others from their time, the remainder of the book is organized geographically rather than chronologically, in order to set the works it discusses into their local context. Thus, Chapter 4 covers the spread of perspective among the artists and artisans of 15th-century Italy, including the works of Luca Pacioli and Daniele Barbaro, while Chapter 5 concerns developments in Northern Europe in the same timeframe by Albrecht Dürer, Wenzel Jamnitzer, and Paul Vredeman de Vries, among others.
In what reviewer Riccardo Bellé calls "the core of the book", chapters 6 through 12 cover the developments of the theory by Guidobaldo del Monte, Simon Stevin, Willem 's Gravesande, and Brook Taylor.Again, after an initial chapter on del Monte's discovery of the vanishing point and Stevin's mathematical explication of del Monte's work, these chapters are divided geographically. Chapter 7 concerns the Netherlands, including the Dutch painters of the 17th century, the book on perspective by Samuel Marolois , and the work of 's Gravesande. Chapter 8 returns to Italy, and the work of architects and stage designers there, including Andrea Pozzo among the Jesuits. Chapter 9 covers over 40 works from France and Belgium, including the anonymously-published work of Jean Du Breuil, who brought the Jesuit knowledge of architecture from Italy to France, and the work on anamorphosis by Jean François Niceron. This chapter also covers Girard Desargues, although it disagrees with the widely-held opinion that Desargues was the inventor of projective geometry. Chapter 10, the longest of the book, concerns Britain, including Taylor, and his followers. Chapters 11 and 12 both concern the German-speaking countries, with Chapter 12 focusing on Johann Heinrich Lambert, who "concluded the process of understanding the geometry behind perspective by creating perspectival geometry".
A penultimate chapter concerns Gaspard Monge, the development of descriptive geometry, and its relation to the earlier perspective geometry and projective geometry. After a final summary chapter, the book includes four appendices and two bibliographies. The book is illustrated with over 600 black and white images, some from the works described and others new-created visualizations of their mathematical concepts,with older diagrams consistently relabeled to make their common features more apparent.
From this history, reviewer Jeremy Gray draws several interesting conclusions: that, after their initial joint formulation, the mathematical and artistic aspects of the subject remained more or less separate, with later developments in mathematics having little influence on artistic practice, that (despite frequent accounts of their being directly connected) the earlier work on perspective geometry had little influence on the creation of projective geometry, and that despite covering so many contributors to this history, Andersen could find no women among them.
Reviewer Christa Binderdescribes this book as Kirsti Andersen's life work and the "definitive reference work on perspective, a classic in its field". Riccardo Bellé recommends the book to "a wide range of scholars, especially historians of mathematics, historians of art, historians of architecture", but also to practitioners of architecture, engineering, or perspective art, and to art teachers. Philip J. Davis recommends it to anyone who wishes to understand the roots of contemporary computer graphics. Gray calls it "a remarkable piece of historical research" that "will surely become the definitive text on the subject".
However, although finding the book clearly written and comprehensive as a history of perspective, reviewer Greg St. George warns against trying to use this book as an introduction to the mathematics of perspective, for which a more focused text would be more appropriate.Similarly, Judith V. Field finds that the book's attempts to make the mathematics more clear, by unifying its notation and terminology and basing its explanations on modern mathematical treatments, tend to muddle its treatment of the history and historical sources of the subject. Field also takes fault with the book's superficial and dismissive treatment of Desargues, with its uncritical reliance on modern sources that Field considers dubious such as the work of Morris Kline, with its "coy refusal" to draw conclusions from the story it tells, and with its publisher's poor copyediting.
François d'Aguilon was a Jesuit, mathematician, physicist, and architect from the Spanish Netherlands.
Girard Desargues was a French mathematician and engineer, who is considered one of the founders of projective geometry. Desargues' theorem, the Desargues graph, and the crater Desargues on the Moon are named in his honour.
In projective geometry, Desargues's theorem, named after Girard Desargues, states:
Geometry of Complex Numbers: Circle Geometry, Moebius Transformation, Non-Euclidean Geometry is an undergraduate textbook on geometry, whose topics include circles, the complex plane, inversive geometry, and non-Euclidean geometry. It was written by Hans Schwerdtfeger, and originally published in 1962 as Volume 13 of the Mathematical Expositions series of the University of Toronto Press. A corrected edition was published in 1979 in the Dover Books on Advanced Mathematics series of Dover Publications (ISBN 0-486-63830-8). The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries.
Mario Bettinus was an Italian Jesuit philosopher, mathematician and astronomer. The lunar crater Bettinus was named after him by Giovanni Riccioli in 1651. His Apiaria Universae Philosophiae Mathematicae is an encyclopedic collection of mathematical curiosities. This work had been reviewed by Christoph Grienberger. Bettini was one of the fiercest Jesuit critics of Cavalieri's method of Indivisibles.
In geometry and in its applications to drawing, a perspectivity is the formation of an image in a picture plane of a scene viewed from a fixed point.
De prospectiva pingendi is the earliest and only pre-1500 Renaissance treatise solely devoted to the subject of perspective. It was written by the Italian master Piero della Francesca in the mid-1470s to 1480s, and possibly by about 1474. Despite its Latin title, the opus is written in Italian.
Kirsti Andersen, published under the name Kirsti Pedersen, is a Danish historian of mathematics. She is an Associate Professor of the History of Science at Aarhus University, where she had her Candidate examination in 1967.
Sherman Kopald Stein is an American mathematician and an author of mathematics textbooks. He is a professor emeritus at the University of California, Davis. His writings have won the Lester R. Ford Award and the Beckenbach Book Prize.
Hazel Perfect was a British mathematician specialising in combinatorics.
Viewpoints: Mathematical Perspective and Fractal Geometry in Art is a textbook on mathematics and art. It was written by mathematicians Marc Frantz and Annalisa Crannell, and published in 2011 by the Princeton University Press (ISBN 9780691125923). The Basic Library List Committee of the Mathematical Association of America has recommended it for inclusion in undergraduate mathematics libraries.
Complexities: Women in Mathematics is an edited volume on women in mathematics that "contains the stories and insights of more than eighty female mathematicians". It was edited by Bettye Anne Case and Anne M. Leggett, based on a collection of material from the Newsletter of the Association for Women in Mathematics, and published by Princeton University Press in 2005 (ISBN 0-691-11462-5).
Polyhedra is a book on polyhedra, by Peter T. Cromwell. It was published by in 1997 by the Cambridge University Press, with an unrevised paperback edition in 1999.
Algorithmic Geometry is a textbook on computational geometry. It was originally written in the French language by Jean-Daniel Boissonnat and Mariette Yvinec, and published as Géometrie algorithmique by Edusciences in 1995. It was translated into English by Hervé Brönnimann, with improvements to some proofs and additional exercises, and published by the Cambridge University Press in 1998.
Computability in Analysis and Physics is a monograph on computable analysis by Marian Pour-El and J. Ian Richards. It was published by Springer-Verlag in their Perspectives in Mathematical Logic series in 1989, and reprinted by the Association for Symbolic Logic and Cambridge University Press in their Perspectives in Logic series in 2016.
Mathematical Excursions: Side Trips along Paths Not Generally Traveled in Elementary Courses in Mathematics is a book on popular mathematics. It was written by Helen Abbot Merrill, published in 1933 by the Norwood Press, and reprinted (posthumously) by Dover Publications in 1957.
Geometric Exercises in Paper Folding is a book on the mathematics of paper folding. It was written by Indian mathematician T. Sundara Row, first published in India in 1893, and later republished in many other editions. Its topics include paper constructions for regular polygons, symmetry, and algebraic curves. According to historian of mathematics Michael Friedman, it became "one of the main engines of the popularization of folding as a mathematical activity".
A Topological Picturebook is a book on mathematical visualization in low-dimensional topology by George K. Francis. It was originally published by Springer in 1987, and reprinted in paperback in 2007. The Basic Library List Committee of the Mathematical Association of America has recommended its inclusion in undergraduate mathematics libraries.
Judith Veronica Field is a British historian of science with interests in mathematics and the impact of science in art, an honorary visiting research fellow in the Department of History of Art of Birkbeck, University of London, former president of the British Society for the History of Mathematics, and president of the Leonardo da Vinci Society.
Snezana Lawrence is a Yugoslav and British historian of mathematics and a senior lecturer in mathematics and design engineering at Middlesex University.