Download or read book Outer Billiards on Kites AM 171 written by Richard Evan Schwartz and published by Princeton University Press. This book was released on 2009-10-25 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Outer billiards is a basic dynamical system defined relative to a convex shape in the plane. B. H. Neumann introduced this system in the 1950s, and J. Moser popularized it as a toy model for celestial mechanics. All along, the so-called Moser-Neumann question has been one of the central problems in the field. This question asks whether or not one can have an outer billiards system with an unbounded orbit. The Moser-Neumann question is an idealized version of the question of whether, because of small disturbances in its orbit, the Earth can break out of its orbit and fly away from the Sun. In Outer Billiards on Kites, Richard Schwartz presents his affirmative solution to the Moser-Neumann problem. He shows that an outer billiards system can have an unbounded orbit when defined relative to any irrational kite. A kite is a quadrilateral having a diagonal that is a line of bilateral symmetry. The kite is irrational if the other diagonal divides the quadrilateral into two triangles whose areas are not rationally related. In addition to solving the basic problem, Schwartz relates outer billiards on kites to such topics as Diophantine approximation, the modular group, self-similar sets, polytope exchange maps, profinite completions of the integers, and solenoids--connections that together allow for a fairly complete analysis of the dynamical system.
Download or read book Man Play and Games written by Roger Caillois and published by University of Illinois Press. This book was released on 2001 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to Roger Caillois, play is an occasion of pure waste. In spite of this - or because of it - play constitutes an essential element of human social and spiritual development. In this study, the author defines play as a free and voluntary activity that occurs in a pure space, isolated and protected from the rest of life.
Download or read book Geometry and Billiards written by Serge Tabachnikov and published by American Mathematical Soc.. This book was released on 2005 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. Topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course. Minimum prerequisites are the standard material covered in the first two years of college mathematics (the entire calculus sequence, linear algebra). However, readers should show some mathematical maturity and rely on their mathematical common sense. A unique feature of the book is the coverage of many diverse topics related to billiards, for example, evolutes and involutes of plane curves, the four-vertex theorem, a mathematical theory of rainbows, distribution of first digits in various sequences, Morse theory, the Poincare recurrence theorem, Hilbert's fourth problem, Poncelet porism, and many others. There are approximately 100 illustrations. The book is suitable for advanced undergraduates, graduate students, and researchers interested in ergodic theory and geometry. This volume has been copublished with the Mathematics Advanced Study Semesters program at Penn State.
Download or read book Dictionary of the British English Spelling System written by Greg Brooks and published by Open Book Publishers. This book was released on 2015-03-30 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will tell all you need to know about British English spelling. It's a reference work intended for anyone interested in the English language, especially those who teach it, whatever the age or mother tongue of their students. It will be particularly useful to those wishing to produce well-designed materials for teaching initial literacy via phonics, for teaching English as a foreign or second language, and for teacher training. English spelling is notoriously complicated and difficult to learn; it is correctly described as much less regular and predictable than any other alphabetic orthography. However, there is more regularity in the English spelling system than is generally appreciated. This book provides, for the first time, a thorough account of the whole complex system. It does so by describing how phonemes relate to graphemes and vice versa. It enables searches for particular words, so that one can easily find, not the meanings or pronunciations of words, but the other words with which those with unusual phoneme-grapheme/grapheme-phoneme correspondences keep company. Other unique features of this book include teacher-friendly lists of correspondences and various regularities not described by previous authorities, for example the strong tendency for the letter-name vowel phonemes (the names of the letters ) to be spelt with those single letters in non-final syllables.
Download or read book Discovering Geometry written by Michael Serra and published by . This book was released on 2003-03-01 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Letters and Social Aims written by Ralph Waldo Emerson and published by London. This book was released on 1883 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Psychoanalytic Perspectives on Puberty and Adolescence written by Gertraud Diem-Wille and published by Routledge. This book was released on 2020-12-30 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Puberty is a time of tumultuous transition from childhood to adulthood activated by rapid physical changes, hormonal development and explosive activity of neurons. This book explores puberty through the parent-teenager relationship, as a "normal state of crisis", lasting several years and with the teenager oscillating between childlike tendencies and their desire to become an adult. The more parents succeed in recognizing and experiencing these new challenges as an integral, ineluctable emotional transformative process, the more they can allow their children to become independent. In addition, parents who can also see this crisis as a chance for their own further development will be ultimately enriched by this painful process. They can face up to their own aging as they take leave of youth with its myriad possibilities, accepting and working through a newfound rivalry with their sexually mature children, thus experiencing a process of maturity, which in turn can set an example for their children. This book is based on rich clinical observations from international settings, unique within the field, and there is an emphasis placed by the author on the role of the body in self-awareness, identity crises and gender construction. It will be of great interest to psychoanalysts, psychotherapists, parents and carers, as well as all those interacting with adolescents in self, family and society.
Download or read book Poncelet Porisms and Beyond written by Vladimir Dragović and published by Springer Science & Business Media. This book was released on 2011-05-02 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to present, in a complete and comprehensive way, areas of current research interlacing around the Poncelet porism: dynamics of integrable billiards, algebraic geometry of hyperelliptic Jacobians, and classical projective geometry of pencils of quadrics. The most important results and ideas, classical as well as modern, connected to the Poncelet theorem are presented, together with a historical overview analyzing the classical ideas and their natural generalizations. Special attention is paid to the realization of the Griffiths and Harris programme about Poncelet-type problems and addition theorems. This programme, formulated three decades ago, is aimed to understanding the higher-dimensional analogues of Poncelet problems and the realization of the synthetic approach of higher genus addition theorems.
Download or read book The Silicon Web written by Michael G. Raymer and published by CRC Press. This book was released on 2009-06-23 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: The technology behind computers, fiber optics, and networks did not originate in the minds of engineers attempting to build an Internet. The Internet is a culmination of intellectual work by thousands of minds spanning hundreds of years. We have built concept upon concept and technology upon technology to arrive at where we are today, in a world co
Download or read book Improvisation for the Theater written by Viola Spolin and published by . This book was released on 1983 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory and foundation - Exercises - Children and the theatre - The formal theatre_
Download or read book The Sicilian written by Mario Puzo and published by Ballantine Books. This book was released on 2004-09-28 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: After Mario Puzo wrote his internationally acclaimed The Godfather, he has often been imitated but never equaled. Puzo's classic novel, The Sicilian, stands as a cornerstone of his work—a lushly romantic, unforgettable tale of bloodshed, justice, and treachery. . . . The year is 1950. Michael Corleone is nearing the end of his exile in Sicily. The Godfather has commanded Michael to bring a young Sicilian bandit named Salvatore Guiliano back with him to America. But Guiliano is a man entwined in a bloody web of violence and vendettas. In Sicily, Guiliano is a modern day Robin Hood who has defied corruption—and defied the Cosa Nostra. Now, in the land of mist-shrouded mountains and ancient ruins, Michael Corleone's fate is entwined with the dangerous legend of Salvatore Guiliano: warrior, lover, and the ultimate Siciliano. Praise for The Sicilian “Puzo is a master storyteller.”—USA Today “The Balzac of the mafia.”—Time “An accomplished and imaginative writer.”—Los Angeles Times
Download or read book The Rosy Crucifixion Sexus written by Henry Miller and published by Miller, Henry. This book was released on 1987 with total page 992 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book of a trilogy of novels known collectively as "The Rosy Crucifixion." It is autobiographical and tells the story of Miller's first tempestuous marriage and his relentless sexual exploits in New York. The other books are "Plexus" and "Nexus."
Download or read book Some Adventures in Euclidean Geometry written by Michael de Villiers and published by Dynamic Mathematics Learning. This book was released on 2009-09-08 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book seeks to actively involve the reader in the heuristic processes of conjecturing, discovering, formulating, classifying, defining, refuting, proving, etc. within the context of Euclidean geometry. The book deals with many interesting and beautiful geometric results, which have only been discovered during the past 300 years such as the Euler line, the theorems of Ceva, Napoleon, Morley, Miquel, Varignon, etc. Extensive attention is also given to the classification of the quadrilaterals from the symmetry of a side-angle duality. Many examples lend themselves excellently for exploration on computer with dynamic geometry programs such as Sketchpad. The book is addressed primarily to university or college lecturers involved in the under-graduate or in-service training of high school mathematics teachers, but may also interest teachers who are looking for enrichment material, and gifted high school mathematics pupils.
Download or read book Lord Minto written by John Buchan and published by London : Thomas Nelson. This book was released on 1924 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Play of Man written by Karl Groos and published by . This book was released on 1908 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Autobiography written by Herbert Spencer and published by . This book was released on 1904 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: This autobiography is published as it was left by Mr. Spencer, with a few modifications, the most important of which relates to the division of the volumes ... the first volume end[s] with the termination of his miscellaneous work and the second volume begin[s] with the planning of the Synthetic Philosophy.
