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In the Preface to Even though I knew beforehand many of the illustrations and
most of the authors presented in Peterson's new book, I still
read it with great pleasure. It is a visual and creative book,
presenting the multiple and unimaginable intersections of mathematics
and art. Containing more than 250 illustrations and photographs
of artworks -- 28 in full color -- produced by many contemporary
mathematicians who are also artists working in media spanning
from metals to glass to snow, The book´s poetic title echoes thoughts of the Dutch
graphic artist M.C. Escher, who sought to capture the elusive
notion of infinity in visual images. As Doris Schattschneider
states in her splendid book
The contents of Peterson's book include "Gallery Visits"; "Theorems in Stone"; "A Place in Space"; "Plane Folds"; " Grid Fields"; "Crystal Visions"; "Strange Sides"; "Minimal Snow"; "Points of View"; and "Fragments." In the first chapter of the book, the fascinating torso carved from limestone by Nat Friedman appears as an intriguing example of the series in which Friedman explores the "combination of form, space and light." The second chapter, "Theorems in Stone", is dedicated to the original sculptor and mathematician Helaman Ferguson, who not only works with computers but also carves marble and moulds bronze into wonderful mathematically inspired networks. "A Place in Space" starts with the famous book "Plane Folds", the fourth chapter, is dedicated
to the art of origami. Many interesting origami tessellations
are presented, not only made folding paper but also pleating
silk or other textile materials. In the fifth chapter, "Grid
Fields", the vast mosaic of square tiles at the entrance
to the Downsview subway station in Toronto, Canada, designed
by Arlene Stamp, is exhaustively analyzed. Few people noticed
that her remarkable design is based on the decimal digits of
the number "Crystal visions" is, in my opinion, the most interesting of all chapters, starting from the painted canvases and three-dimensional models of architectural structures designed by Tony Robbin up to Roger Penrose famous non-periodic tilings that explain the strange five-fold symmetry found in quasi-crystals. Following from this, the seventh chapter is based on the intriguing mathematical form known as the Möbius strip, which has inspired beautiful giant sculptures. These sculptures lie mostly in plazas and gardens and were made of different materials like re-painted steel, granite, wood, stainless steel, stone, by artists such as Charles O. Perry, Benigna Chilla, John Robinson and many others. "Minimal Snow" presents minimal surfaces, which are those for which any distortion, no matter how small, increases its area. A soap film is a model of such a surface. In 1999, the international Snow Sculpture Championship was held at the Rocky Mountains of Colorado, USA. The chosen shape was the central portion of the Costa surface, named for the Brazilian mathematician Celso J. Costa, who discovered the equations of this minimal surface in 1983. The chapter also includes bronze versions of the surface by Helaman Ferguson. Chapter 9, "Points of View", is dedicated to different sorts of complex and beautiful sculptures that look startlingly different from different viewpoints. Among them are the spirolateral designs generated by Robert J. Krawczyk of the College of Architecture at the Illinois Institute of Technology in Chicago, USA. A spirolateral is a line design such that if the first line is one unit long, each successive line is one unit longer than the previous one. The last chapter considers interesting applications of hyperbolic geometry, starting with the well known Escher´s Circle Limit series of prints up to Douglas Dunham computer program to transform one hyperbolic tiling pattern into another. The book ends with a long list of Further Readings for each chapter, opening a wide road for future investigations in this domain of mathematical art.
Flatland:
A Romance of Many Dimensions. 1884. New York: Dover Publications.Peterson, Ivars. 2001. ______. 1998. Schnattschneider, Doris. 1992.
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