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. [1]
The first seven chapters of the book concern perspectivity, while its final two concern fractals and their geometry. [1] [2] Topics covered within the chapters on perspectivity include coordinate systems for the plane and for Euclidean space, similarity, angles, and orthocenters, one-point and multi-point perspective, and anamorphic art. [1] [3] In the fractal chapters, the topics include self-similarity, exponentiation, and logarithms, and fractal dimension. Beyond this mathematical material, the book also describes methods for artists to depict scenes in perspective, and for viewers of art to understand the perspectives in the artworks they see, [1] for instance by finding the optimal point from which to view an artwork. [2] The chapters are ordered by difficulty, and begin with experiments that the students can perform on their own to motivate the material in each chapter. [3]
The book is heavily illustrated by artworks and photography (such as the landscapes of Ansel Adams) and includes a series of essays or interviews by contemporary artists on the mathematical content of their artworks. [1] [3] An appendix contains suggestions aimed at teachers of this material. [3]
Viewpoints is intended as a textbook for mathematics classes aimed at undergraduate liberal arts students, [1] [2] [4] as a way to show these students how geometry can be used in their everyday life. [2] However, it could even be used for high school art students, [2] [3] and reviewer Paul Kelley writes that "it will be of value to anyone interested in an elementary introduction to the mathematics and practice of perspective drawing". [2] It differs from many other liberal arts mathematics textbooks in its relatively narrow focus on geometry and perspective, and its avoidance of more well-covered ground in mathematics and the arts such as symmetry and the geometry of polyhedra. [2]
Although reviewer Blake Mellor complains that the connection between the material on perspective and on fractal geometry "feels forced", he concludes that "this is an excellent text". [4] Reviewer Paul Kelley writes that the book's "step-by-step progression" through its topics makes it "readable [and] easy-to-follow", and that "Students can learn a great deal from this book." [2] Reviewer Alexander Bogomolny calls it "an elegant fusion of mathematical ideas and practical aspects of fine art". [1]
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.
Annalisa Crannell is an American mathematician, and an expert in the mathematics of water waves, chaos theory, and geometric perspective. She is a professor of mathematics at Franklin & Marshall College.
Treks into Intuitive Geometry: The World of Polygons and Polyhedra is a book on geometry, written as a discussion between a teacher and a student in the style of a Socratic dialogue. It was written by Japanese mathematician Jin Akiyama and science writer Kiyoko Matsunaga, and published by Springer-Verlag in 2015 (ISBN 978-4-431-55841-5).
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.
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Symmetry in Mechanics: A Gentle, Modern Introduction is an undergraduate textbook on mathematics and mathematical physics, centered on the use of symplectic geometry to solve the Kepler problem. It was written by Stephanie Singer, and published by Birkhäuser in 2001.
Introduction to the Theory of Error-Correcting Codes is a textbook on error-correcting codes, by Vera Pless. It was published in 1982 by John Wiley & Sons, with a second edition in 1989 and a third in 1998. The Basic Library List Committee of the Mathematical Association of America has rated the book as essential for inclusion in undergraduate mathematics libraries.
Timothy P. Chartier is Joseph R. Morton Professor of Mathematics and Computer Science at Davidson College, known for his expertise in sports analytics and bracketology, for his popular mathematics books, and for the "mime-matics" shows combining mime and mathematics that he and his wife Tanya have staged.
The Tower of Hanoi – Myths and Maths is a book in recreational mathematics, on the tower of Hanoi, baguenaudier, and related puzzles. It was written by Andreas M. Hinz, Sandi Klavžar, Uroš Milutinović, and Ciril Petr, and published in 2013 by Birkhäuser, with an expanded second edition in 2018. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries.
Making Mathematics with Needlework: Ten Papers and Ten Projects is an edited volume on mathematics and fiber arts. It was edited by sarah-marie belcastro and Carolyn Yackel, and published in 2008 by A K Peters, based on a meeting held in 2005 in Atlanta by the American Mathematical Society.
The Mathematics of Chip-Firing is a textbook in mathematics on chip-firing games and abelian sandpile models. It was written by Caroline Klivans, and published in 2018 by the CRC Press.
Combinatorics of Experimental Design is a textbook on the design of experiments, a subject that connects applications in statistics to the theory of combinatorial mathematics. It was written by mathematician Anne Penfold Street and her daughter, statistician Deborah Street, and published in 1987 by the Oxford University Press under their Clarendon Press imprint.
Journey into Geometries is a book on non-Euclidean geometry. It was written by Hungarian-Australian mathematician Márta Svéd, and published in 1991 by the Mathematical Association of America in their MAA Spectrum book series.
The Secrets of Triangles: A Mathematical Journey is a popular mathematics book on the geometry of triangles. It was written by Alfred S. Posamentier and Ingmar Lehmann, and published in 2012 by Prometheus Books.
Tatiana Shubin is a Soviet and American mathematician known for her work developing math circles, social structures for the mathematical enrichment of secondary-school students, especially among the Navajo and other Native American people. She is a professor of mathematics at San José State University in California.
Geometric Constructions is a mathematics textbook on constructible numbers, and more generally on using abstract algebra to model the sets of points that can be created through certain types of geometric construction, and using Galois theory to prove limits on the constructions that can be performed. It was written by George E. Martin, and published by Springer-Verlag in 1998 as volume 81 of their Undergraduate Texts in Mathematics book series.
The Symmetries of Things is a book on mathematical symmetry and the symmetries of geometric objects, aimed at audiences of multiple levels. It was written over the course of many years by John Horton Conway, Heidi Burgiel, and Chaim Goodman-Strauss, and published in 2008 by A K Peters. Its critical reception was mixed, with some reviewers praising it for its accessible and thorough approach to its material and for its many inspiring illustrations, and others complaining about its inconsistent level of difficulty, overuse of neologisms, failure to adequately cite prior work, and technical errors.
Theoni Pappas is an American mathematics teacher known for her books and calendars concerning popular mathematics.
Curvature of Space and Time, with an Introduction to Geometric Analysis is an undergraduate-level textbook for mathematics and physics students on differential geometry, focusing on applications to general relativity. It was written by Iva Stavrov, based on a course she taught at the 2013 Park City Mathematics Institute and subsequently at Lewis & Clark College, and was published in 2020 by the American Mathematical Society, as part of their Student Mathematical Library book series.
Deirdre Longacher Smeltzer is an American mathematician, mathematics educator, textbook author, and academic administrator. A former professor, dean, and vice president at Eastern Mennonite University, she is Senior Director for Programs at the Mathematical Association of America.
