How can one visualize a curve that fills the entire plane or all of space? Can a polyhedron be smoothly turned inside out? What is the projective plane? What does four-dimensional space look like? Can soap bubbles exist that are not spherical? How can one better understand the structure of vortices and currents? In this book you will experience mathematics from the visual point of view, where fascinating images, many of them appearing in print for the first time, provide answers to the above questions. Every picture is accompanied by a brief explanatory text along with numerous references and web links for further reading. This book is intended for all friends of mathematics- students, teachers, amateurs, and professionals-who want to see something beyond dry text and endless formulas. It will provide inspiration for further pursuit of topics in mathematics that may previously have seemed inaccessible. You will get to know mathematics from a totally new and colorful viewpoint. Enjoy the beauty and fascination of mathematics in over 300 pages richly illustrated with more than 1000 figures on the following topics: ¿ Polyhedral Models ¿ Geometry in the Plane ¿ Problems New and Old ¿ Formulas and Numbers ¿ Functions and Limits ¿ Curves and Knots ¿ Geometry and Topology of Surfaces ¿ Minimal Surfaces and Soap Bubbles ¿ Tilings and Packings ¿ Space Forms and Dimension ¿ Graphs and Incidence Geometry ¿ Flexible Shapes ¿ Fractals ¿ Maps and Mappings ¿ Forms and Processes in Nature and Technology

Georg Glaeser is professor of mathematics and geometry at the University of Applied Art in Vienna and the author of numerous books on computational geometry. Konrad Polthier is professor of mathematics at the Free University of Berlin and the DFG Research Center Matheon. Springer has published a number of his books on mathematical visualization as well as entertaining videos on mathematics, including the prizewinning MESH and the collection of films from the MathFilm Festival 2008.