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Projective geometry and projective metrics

Geometry, Projective. --- Geometry, Modern. --- Modern geometry --- Sphere --- Projective geometry --- Geometry, Modern

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Geometry --- Geometry, Modern --- Convex bodies. --- Convex surfaces --- 514.1 --- Convex bodies --- #TCPW W1.0 --- #TCPW W1.1 --- Modern geometry --- Sphere --- Convex areas --- Convex domains --- Surfaces --- General geometry --- Convex surfaces. --- Geometry, Modern. --- 514.1 General geometry --- Géometrie convexe

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This text uses mathematics to analyze games of chance and skill. Roulette, craps, blackjack, backgammon, poker, bridge, lotteries and horse races are considered here in a way that reveals their mathematical aspects. The tools used include probability, expectation, and game theory.

Geometry, Modern. --- Modern geometry --- Sphere --- Games of chance (Mathematics) --- Gambling problem (Mathematics) --- Chance --- Game theory --- Mathematics --- Geometry --- Geometry, Projective. --- Graphic methods. --- Competitions. --- Data processing. --- Geometry, projective --- Geometry, Modern --- Géometrie descriptive --- Géometrie descriptive --- 51-8 --- 51-8 Mathematical games and recreations --- Mathematical games and recreations --- Mathematic --- Competitions --- Geometry, modern --- Collection de problemes --- Olympiades mathematiques --- Histoire des mathematiques --- Geometrie

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Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces, convex sets, etc., crucial ideas and above all abstract concepts needed for attaining the results are elucidated. These are conceptual notions, each built "above" the preceding and permitting an increase in abstraction, represented metaphorically by Jacob's ladder with its rungs: the 'ladder' in the Old Testament, that angels ascended and descended... In all this, the aim of the book is to demonstrate to readers the unceasingly renewed spirit of geometry and that even so-called "elementary" geometry is very much alive and at the very heart of the work of numerous contemporary mathematicians. It is also shown that there are innumerable paths yet to be explored and concepts to be created. The book is visually rich and inviting, so that readers may open it at random places and find much pleasure throughout according their own intuitions and inclinations. Marcel Berger is t he author of numerous successful books on geometry, this book once again is addressed to all students and teachers of mathematics with an affinity for geometry.

Geometry, Differential. --- Geometry. --- Mathematics. --- Geometry, Differential --- Mathematics --- Geometry --- Physical Sciences & Mathematics --- Geometry, Modern. --- Modern geometry --- Dynamics. --- Ergodic theory. --- Convex geometry. --- Discrete geometry. --- Differential geometry. --- History. --- Combinatorics. --- History of Mathematical Sciences. --- Convex and Discrete Geometry. --- Differential Geometry. --- Dynamical Systems and Ergodic Theory. --- Sphere --- Discrete groups. --- Global differential geometry. --- Differentiable dynamical systems. --- Combinatorics --- Algebra --- Mathematical analysis --- Groups, Discrete --- Infinite groups --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Euclid's Elements --- Discrete mathematics --- Convex geometry . --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Differential geometry --- Combinatorial geometry --- Annals --- Auxiliary sciences of history --- Math --- Science