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"From nothing I have created a new different world,” wrote János Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture. The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics. Audience This book is intended for those who teach, study, and do research in geometry and history of mathematics. Cultural historians, physicists, and computer scientists will also find it an important source of information.

Geometry, Non-Euclidean. --- Mathematics. --- Math --- Science --- Non-Euclidean geometry --- Geometry --- Parallels (Geometry) --- Foundations --- Geometry. --- Global differential geometry. --- Cell aggregation --- History of Mathematical Sciences. --- Differential Geometry. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Classical and Quantum Gravitation, Relativity Theory. --- Aggregation, Cell --- Cell patterning --- Cell interaction --- Microbial aggregation --- Geometry, Differential --- Mathematics --- Euclid's Elements --- History. --- Differential geometry. --- Manifolds (Mathematics). --- Complex manifolds. --- Gravitation. --- Field theory (Physics) --- Matter --- Physics --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Analytic spaces --- Manifolds (Mathematics) --- Topology --- Differential geometry --- Annals --- Auxiliary sciences of history --- Properties --- Bolyai, János, --- Boi︠a︡i, I︠A︡nosh,