the three body problem from pythagoras to hawking

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The Three Body Problem From Pythagoras To Hawking

Author : Mauri Valtonen
ISBN : 9783319227269
Genre : Science
File Size : 65. 42 MB
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This book, written for a general readership, reviews and explains the three-body problem in historical context reaching to latest developments in computational physics and gravitation theory. The three-body problem is one of the oldest problems in science and it is most relevant even in today’s physics and astronomy. The long history of the problem from Pythagoras to Hawking parallels the evolution of ideas about our physical universe, with a particular emphasis on understanding gravity and how it operates between astronomical bodies. The oldest astronomical three-body problem is the question how and when the moon and the sun line up with the earth to produce eclipses. Once the universal gravitation was discovered by Newton, it became immediately a problem to understand why these three-bodies form a stable system, in spite of the pull exerted from one to the other. In fact, it was a big question whether this system is stable at all in the long run. Leading mathematicians attacked this problem over more than two centuries without arriving at a definite answer. The introduction of computers in the last half-a-century has revolutionized the study; now many answers have been found while new questions about the three-body problem have sprung up. One of the most recent developments has been in the treatment of the problem in Einstein’s General Relativity, the new theory of gravitation which is an improvement on Newton’s theory. Now it is possible to solve the problem for three black holes and to test one of the most fundamental theorems of black hole physics, the no-hair theorem, due to Hawking and his co-workers.

The Three Body Problem

Author : Mauri Valtonen
ISBN : 0521852242
Genre : Mathematics
File Size : 30. 43 MB
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This book surveys statistical and perturbation methods for the solution of the general three body problem.

Poincar And The Three Body Problem

Author : June Barrow-Green
ISBN : 0821803670
Genre : Mathematics
File Size : 86. 38 MB
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The idea of chaos figures prominently in mathematics today. It arose in the work of one of the greatest mathematicians of the late 19th century, Henri Poincare, on a problem in celestial mechanics: the three body problem. This ancient problem--to describe the paths of three bodies in mutual gravitational interaction--is one of those which is simple to pose but impossible to solve precisely. Poincare's famous memoir on the three body problem arose from his entry in the competition celebrating the 60th birthday of King Oscar of Sweden and Norway. His essay won the prize and was set up in print as a paper in Acta Mathematica when it was found to contain a deep and critical error. In correcting this error Poincare discovered mathematical chaos, as is now clear from Barrow-Green's pioneering study of a copy of the original memoir annotated by Poincare himself, recently discovered in the Institut Mittag-Leffler in Stockholm. Poincare and the Three Body Problem opens with a discussion of the development of the three body problem itself and Poincare's related earlier work. The book also contains intriguing insights into the contemporary European mathematical community revealed by the workings of the competition. After an account of the discovery of the error and a detailed comparative study of both the original memoir and its rewritten version, the book concludes with an account of the final memoir's reception, influence and impact, and an examination of Poincare's subsequent highly influential work in celestial mechanics.

The Three Body Problem

Author : Catherine Shaw
ISBN : 9780749014445
Genre : Fiction
File Size : 85. 25 MB
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Cambridge, 1888. When schoolmistress Vanessa Duncan learns of a murder at St John's College, little does she know that she will become deeply entangled in the mystery. Dr Geoffrey Akers, Fellow in Pure Mathematics, has been found dead, struck down by a violent blow to the head. What could provoke such a brutal act? Vanessa, finding herself in amongst Cambridge's brightest scholarly minds, discovers that the motive may lie in mathematics itself. Drawn closer to the case by a blossoming friendship with mathematician Arthur Weatherburn, Vanessa begins to investigate. When she learns of Sir Isaac Newton's elusive 'n-body problem' and the prestigious prize offered to anyone with a solution, things begin to make sense. But with further deaths occurring and the threat of an innocent man being condemned, Vanessa must hurry with her calculations...

The Great Equations Breakthroughs In Science From Pythagoras To Heisenberg

Author : Robert P. Crease
ISBN : 9780393337938
Genre : Mathematics
File Size : 61. 43 MB
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Shares behind-the-scenes stories for ten of the most significant equations in human history, covering a range of topics, from Feynman's statement about Maxwell's pivotal electromagnetic equations and the influence of Newton's law of gravitation to the reason Euler's formula has been called "God's equation" and Heisenberg's uncertainty principle. 20,000 first printing.

Quantum Physics Mini Black Holes And The Multiverse

Author : Yasunori Nomura
ISBN : 9783319417097
Genre : Science
File Size : 80. 91 MB
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"Modern physics is rife with provocative and fascinating ideas, from quantum mechanics to the multiverse. But as interesting as these concepts are, they are also easy to understand. This book, written with deft hands by true experts in the field, helps to illuminate some of the most important and game-changing ideas in physics today." Sean M. Carroll "The Multiversal book series is equally unique, providing book-length extensions of the lectures with enough additional depth for those who truly want to explore these fields, while also providing the kind of clarity that is appropriate for interested lay people to grasp the general principles involved. " Lawrence M. Krauss This book explores, explains and debunks some common misconceptions about quantum physics, particle physics, space-time, and Multiverse cosmology. It seeks to separate science from pseudoscience. The material is presented in layperson-friendly language, followed by additional technical sections which explain basic equations and principles. This feature is very attractive to non-expert readers who nevertheless seek a deeper understanding of the theories, and wish to explore beyond just the basic description. Multiversal JourneysTM is a trademark of Farzad Nekoogar and Multiversal Journeys, a 501 (c) (3) nonprofit organization.

Archimedes To Hawking

Author : Clifford Pickover
ISBN : 0199792682
Genre : Science
File Size : 61. 93 MB
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Archimedes to Hawking takes the reader on a journey across the centuries as it explores the eponymous physical laws--from Archimedes' Law of Buoyancy and Kepler's Laws of Planetary Motion to Heisenberg's Uncertainty Principle and Hubble's Law of Cosmic Expansion--whose ramifications have profoundly altered our everyday lives and our understanding of the universe. Throughout this fascinating book, Clifford Pickover invites us to share in the amazing adventures of brilliant, quirky, and passionate people after whom these laws are named. These lawgivers turn out to be a fascinating, diverse, and sometimes eccentric group of people. Many were extremely versatile polymaths--human dynamos with a seemingly infinite supply of curiosity and energy and who worked in many different areas in science. Others had non-conventional educations and displayed their unusual talents from an early age. Some experienced resistance to their ideas, causing significant personal anguish. Pickover examines more than 40 great laws, providing brief and cogent introductions to the science behind the laws as well as engaging biographies of such scientists as Newton, Faraday, Ohm, Curie, and Planck. Throughout, he includes fascinating, little-known tidbits relating to the law or lawgiver, and he provides cross-references to other laws or equations mentioned in the book. For several entries, he includes simple numerical examples and solved problems so that readers can have a hands-on understanding of the application of the law. A sweeping survey of scientific discovery as well as an intriguing portrait gallery of some of the greatest minds in history, this superb volume will engage everyone interested in science and the physical world or in the dazzling creativity of these brilliant thinkers.

Programming Visual Illusions For Everyone

Author : Marco Bertamini
ISBN : 9783319640662
Genre : Technology & Engineering
File Size : 79. 15 MB
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If you find visual illusions fascinating Programming Visual Illusions for Everyone is a book for you. It has some background, some history and some theories about visual illusions, and it describes in some detail twelve illusions. Some are about surfaces, some are about apparent size of objects, some are about colour and some involve movement. This is only one aspect of the book. The other is to show you how you can create these effects on any computer. The book includes a brief introduction to a powerful programming language called Python. No previous experience with programming is necessary. There is also an introduction to a package called PsychoPy that makes it easy to draw on a computer screen. It is perfectly ok if you have never heard the names Python or PsychoPy before. Python is a modern and easy-to-read language, and PsychoPy takes care of all the graphical aspects of drawing on a screen and also interacting with a computer. By the way, both Python and PsychoPy are absolutely free. Is this a book about illusions or about programming? It is both!

Medicynical

Author : Volker Lange
ISBN : 3798514313
Genre : Medical
File Size : 50. 76 MB
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Do cartoons that should speak to the observer flexible endoscope becomes a snake, 'Nessie' swims in themselves without using words require a foreword? the disinfection basin, and Laokoon and sons fight against Do Volker Lange's characteristic drawings, seen at least an endoscope. Seen from Lange's perspective, concepts once by almost everyone involved with medicine, need such as the drawer phenomenon, an onychomycosis, description? and the appendix appear in unique, new light. Does this book render more than a reason to laugh, Lange's cartoons depict the grotesque, the mysterious, more than a moment of 'aha'-experience, more than a and the fantastic: patient and physician drowning in fleeting instant of self-recognition? Do these cartoons liquor during lumbal puncture, a patient actually convey more than ideas that may initially appear even coughing out his lungs, and a neurosurgeon, who finds absurd or bizarre? emptiness when changing his patient's dressings, these Volker Lange has proven in previously published are moments of enlightenment that free us from the bonds material that he knows how to disclose the perhaps of a strictly scientific medicine fixed upon reality. Lange's intentionally overlooked parts of the medical profession. book is a treasure chest of such surrealistic surprises. Here sideswipes against both physicians' vanity and the With a few exceptions, Lange reveals his ideas using weight of the medical industry unmask much more than graphic expression only.

Celestial Sleuth

Author : Donald W. Olson
ISBN : 9781461484035
Genre : Science
File Size : 87. 57 MB
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For a general audience interested in solving mysteries in art, history, and literature using the methods of science, 'forensic astronomy' is a thrilling new field of exploration. Astronomical calculations are the basis of the studies, which have the advantage of bringing to readers both evocative images and a better understanding of the skies. Weather facts, volcano studies, topography, tides, historical letters and diaries, famous paintings, military records, and the friendly assistance of experts in related fields add variety, depth, and interest to the work. The chosen topics are selected for their wide public recognition and intrigue, involving artists such as Vincent van Gogh, Claude Monet, Edvard Munch, and Ansel Adams; historical events such as the Battle of Marathon, the death of Julius Caesar, the American Revolution, and World War II; and literary authors such as Chaucer, Shakespeare, Joyce, and Mary Shelley. This book sets out to answer these mysteries indicated with the means and expertise of astronomy, opening the door to a richer experience of human culture and its relationship with nature. Each subject is carefully analyzed. As an example using the study of sky paintings by Vincent van Gogh, the analytical method would include: - computer calculations of historical skies above France in the 19th century - finding and quoting the clues found in translations of original letters by Van Gogh - making site visits to France to determine the precise locations when Van Gogh set up his easel and what celestial objects are depicted. For each historical event influenced by astronomy, there would be a different kind of mystery to be solved. As an example: - How can the phase of the Moon and time of moonrise help to explain a turning point of the American Civil War - the fatal wounding of Stonewall Jackson at Chancellorsville in 1863? For each literary reference to astronomy, it was determined which celestial objects were being described and making an argument that the author is describing an actual event. For example, what was the date of the moonlit scene when Mary Shelley first had the idea for her novel “Frankenstein?” These and more fun riddles will enchant and delight the fan of art and astronomy.

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