A Mathematical Picture Book, 1st ed. 2024

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, discovering fascinating and never previously published images that offer illustrative examples to the above questions. Every picture is accompanied by a brief explanatory text, references to further reading, and a number of web links where you can obtain further information. 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 pursuing further one or another topic that may previously have seemed inaccessible. You will get to know mathematics from a totally new and colorful viewpoint.

1. Polyhedral Models.- 2. Geometry in the Plane.- 3. Problems New and Old.- 4. Formulas and the Integers.- 5. Functions and Limits.- 6. Curves and Knots.- 7. Geometry and Topology of Surfaces.- 8. Minimal Surfaces and Soap Bubbles.- 9. Tilings and Packings.- 10. Space Forms and Dimension.- 11. Graphs and Incidence Geometry.- 12. Movable Forms.- 13. Fractals.- 14. Maps and Mappings.- 15. Forms and Processes in Nature and Technology.- Picture Credits.- Index.

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.

A visual tour of mathematics More than 1000 coloured illustrations Striking and surprising topics from arithmetics to topology