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Mathematics --- Mathématiques --- Philosophy --- Philosophie --- Philosophy. --- -Math --- Science --- -Philosophy --- Mathématiques --- Mathematics - Philosophy.

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The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, suitable for third or fourth year undergraduates. The basic approach taken is to define hyperbolic lines and develop a natural group of transformations preserving hyperbolic lines, and then study hyperbolic geometry as those quantities invariant under this group of transformations. Topics covered include the upper half-plane model of the hyperbolic plane, Möbius transformations, the general Möbius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the Poincaré disc model, convex subsets of the hyperbolic plane, hyperbolic area, the Gauss-Bonnet formula and its applications. This updated second edition also features: an expanded discussion of planar models of the hyperbolic plane arising from complex analysis; the hyperboloid model of the hyperbolic plane; brief discussion of generalizations to higher dimensions; many new exercises. The style and level of the book, which assumes few mathematical prerequisites, make it an ideal introduction to this subject and provides the reader with a firm grasp of the concepts and techniques of this beautiful part of the mathematical landscape. .

Geometry, Hyperbolic. --- Geometry, Hyperbolic --- Geometry. --- Mathematics. --- Mathematics, general. --- Math --- Science --- Mathematics --- Euclid's Elements --- Géometrie hyperbolique

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The articles included in this book are from the ICTMA 9 conference held in Lisbon, attended by delegates from about 30 countries. This work records the 1999 Lisbon Conference of ICTMA. It contains the selected and edited content of the conference and makes a significant contribution to mathematical modelling which is the significant investigative preliminary to all scientific and technological applications from machinery to satellites and docking of space-ships.Contains the selected and edited content of the 1999 Lisbon Conference of ICTMAMakes a significant contributi

Science --- Mathematics --- Study and teaching --- Technological innovations. --- Math --- Natural science --- Natural sciences --- Science of science --- Sciences

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Religious studies --- Mathematics --- Science --- Theology --- Christian theology --- Theology, Christian --- Christianity --- Religion --- Natural science --- Science of science --- Sciences --- Math --- Natural sciences

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Calculus --- Mathematics --- Analyse (wiskunde) --- Math --- Science --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematical analysis --- Functions --- Geometry, Infinitesimal