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Learn to juggle numbers! This book is the first comprehensive account of the mathematical techniques and results used in the modelling of juggling patterns. This includes all known and many new results about juggling sequences and matrices, the mathematical skeletons of juggling patterns. Many useful and entertaining tips and tricks spice up the mathematical menu presented in this book. There are detailed descriptions of jugglable and attractive juggling sequences, easy zero-gravity juggling, robot juggling, as well as fun juggling of words, anti-balls, and irrational numbers. The book also includes novel, or at least not very well known connections with topics such as bell ringing, knot theory, and the many body problem. In fact, the chapter on mathematical bell ringing has been expanded into the most comprehensive survey in the literature of the mathematics used by bell ringers. Accessible at all levels of mathematical sophistication, this is a book for mathematically wired jugglers, mathematical bell ringers, combinatorists, mathematics educators, and just about anybody interested in beautiful and unusual applications of mathematics.

Sequences (Mathematics) --- Juggling --- Mathematics. --- Juggling -- Mathematics. --- Sequences (Mathematics). --- Engineering & Applied Sciences --- Applied Mathematics --- Mathematics --- Global analysis (Mathematics). --- Analysis. --- Mathematical analysis. --- Analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis --- Mathematical sequences --- Numerical sequences --- Algebra --- Jugglers and juggling --- Legerdemain --- Sleight of hand --- Amusements

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Combinatorial optimization --- Mathematics --- Shoelaces --- Mathematics

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Surfaces --- Geometry, Projective --- 517.4 --- Curved surfaces --- Geometry --- Shapes --- Projective geometry --- Geometry, Modern --- 517.4 Functional determinants. Integral transforms. Operational calculus --- Functional determinants. Integral transforms. Operational calculus

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The projective, Möbius, Laguerre, and Minkowski planes over the real numbers are just a few examples of a host of fundamental classical topological geometries on surfaces. This book summarizes all known major results and open problems related to these classical point-line geometries and their close (nonclassical) relatives. Topics covered include: classical geometries; methods for constructing nonclassical geometries; classifications and characterizations of geometries. This work is related to many other fields including interpolation theory, convexity, the theory of pseudoline arrangements, topology, the theory of Lie groups, and many more. The authors detail these connections, some of which are well-known, but many much less so. Acting both as a reference for experts and as an accessible introduction for graduate students, this book will interest anyone wishing to know more about point-line geometries and the way they interact.

Geometry, Projective. --- Surfaces. --- Curved surfaces --- Geometry --- Shapes --- Projective geometry --- Geometry, Modern