The Kepler Conjecture
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The Kepler Conjecture
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Author : Jeffrey C. Lagarias
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-09
The Kepler Conjecture written by Jeffrey C. Lagarias and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-09 with Mathematics categories.
The Kepler conjecture, one of geometry's oldest unsolved problems, was formulated in 1611 by Johannes Kepler and mentioned by Hilbert in his famous 1900 problem list. The Kepler conjecture states that the densest packing of three-dimensional Euclidean space by equal spheres is attained by the “cannonball" packing. In a landmark result, this was proved by Thomas C. Hales and Samuel P. Ferguson, using an analytic argument completed with extensive use of computers. This book centers around six papers, presenting the detailed proof of the Kepler conjecture given by Hales and Ferguson, published in 2006 in a special issue of Discrete & Computational Geometry. Further supporting material is also presented: a follow-up paper of Hales et al (2010) revising the proof, and describing progress towards a formal proof of the Kepler conjecture. For historical reasons, this book also includes two early papers of Hales that indicate his original approach to the conjecture. The editor's two introductory chapters situate the conjecture in a broader historical and mathematical context. These chapters provide a valuable perspective and are a key feature of this work.
The Six Cornered Snowflake
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Author : Johannes Kepler
language : en
Publisher: Paul Dry Books
Release Date : 2010-01-01
The Six Cornered Snowflake written by Johannes Kepler and has been published by Paul Dry Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-01 with Science categories.
"In 1611, Kepler wrote an essay wondering why snowflakes always had perfect, sixfold symmetry. It's a simple enough question, but one that no one had ever asked before and one that couldn't actually be answered for another three centuries. Still, in trying to work out an answer, Kepler raised some fascinating questions about physics, math, and biology, and now you can watch in wonder as a great scientific genius unleashes the full force of his intellect on a seemingly trivial question, complete with new illustrations and essays to put it all in perspective."—io9, from their list "10 Amazing Science Books That Reveal The Wonders Of The Universe" When snow began to fall while he was walking across the Charles Bridge in Prague late in 1610, the eminent astronomer Johannes Kepler asked himself the following question: Why do snowflakes, when they first fall, and before they are entangled into larger clumps, always come down with six corners and with six radii tufted like feathers? In his effort to answer this charming and never-before-asked question about snowflakes, Kepler delves into the nature of beehives, peapods, pomegranates, five-petaled flowers, the spiral shape of the snail's shell, and the formative power of nature itself. While he did not answer his original question—it remained a mystery for another three hundred years—he did find an occasion for deep and playful thought. "A most suitable book for any and all during the winter and holiday seasons is a reissue of a holiday present by the great mathematician and astronomer Johannes Kepler…Even the endnotes in this wonderful little book are interesting and educationally fun to read."—Jay Pasachoff, The Key Reporter —New English translation by Jacques Bromberg —Latin text on facing pages —An essay, "The Delights of a Roving Mind" by Owen Gingerich —An essay, "On The Six-Cornered Snowflake" by Guillermo Bleichmar —Snowflake illustrations by Capi Corrales Rodriganez —John Frederick Nims' poem "The Six-Cornered Snowflake" —Notes by Jacques Bromberg and Guillermo Bleichmar
The Kepler Conjecture
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Author : Samuel P. Ferguson
language : en
Publisher:
Release Date : 2006
The Kepler Conjecture written by Samuel P. Ferguson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Sphere Packings
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Author : Chuanming Zong
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-08-19
Sphere Packings written by Chuanming Zong and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-08-19 with Mathematics categories.
Sphere packings is one of the most fascinating and challenging subjects in mathematics. In the course of centuries, many exciting results have been obtained, ingenious methods created, related challenging problems proposed, and many surprising connections with other subjects found. This book gives a full account of this fascinating subject, especially its local aspects, discrete aspects, and its proof methods. The book includes both classical and contemporary results and provides a full treatment of the subject.
The Kepler Conjecture
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Author :
language : en
Publisher: Springer
Release Date : 2011-11-09
The Kepler Conjecture written by and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-09 with categories.
The Birth Of Science
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Author : Alex Ely Kossovsky
language : en
Publisher: Springer Nature
Release Date : 2020-08-14
The Birth Of Science written by Alex Ely Kossovsky and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-14 with Science categories.
This book reveals the multi-generational process involved in humanity's first major scientific achievement, namely the discovery of modern physics, and examines the personal lives of six of the intellectual giants involved. It explores the profound revolution in the way of thinking, and in particular the successful refutation of the school of thought inherited from the Greeks, which focused on the perfection and immutability of the celestial world. In addition, the emergence of the scientific method and the adoption of mathematics as the central tool in scientific endeavors are discussed. The book then explores the delicate thread between pure philosophy, grand unifying theories, and verifiable real-life scientific facts. Lastly, it turns to Kepler’s crucial 3rd law and shows how it was derived from a mere six data points, corresponding to the six planets known at the time. Written in a straightforward and accessible style, the book will inform and fascinate all aficionados of science, history, philosophy, and, in particular, astronomy.
Poincare S Prize
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Author : George G. Szpiro
language : en
Publisher: Penguin
Release Date : 2008-07-29
Poincare S Prize written by George G. Szpiro and has been published by Penguin this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-29 with Mathematics categories.
The amazing story of one of the greatest math problems of all time and the reclusive genius who solved it In the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found. Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius.
Conjectures And Refutations
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Author : Karl Raimund Popper
language : en
Publisher: Psychology Press
Release Date : 2002
Conjectures And Refutations written by Karl Raimund Popper and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Philosophy categories.
Conjectures and Refutations is one of Karl Popper's most wide-ranging and popular works, notable not only for its acute insight into the way scientific knowledge grows, but also for applying those insights to politics and to history. It provides one of the clearest and most accessible statements of the fundamental idea that guided his work: not only our knowledge, but our aims and our standards, grow through an unending process of trial and error.
What S Happening In The Mathematical Sciences
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Author : Barry Cipra
language : en
Publisher: American Mathematical Soc.
Release Date :
What S Happening In The Mathematical Sciences written by Barry Cipra and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Science categories.
Mathematicians like to point out that mathematics is universal. In spite of this, most people continue to view it as either mundane (balancing a checkbook) or mysterious (cryptography). This fifth volume of the What's Happening series contradicts that view by showing that mathematics is indeed found everywhere-in science, art, history, and our everyday lives. Here is some of what you'll find in this volume: Mathematics and Science Mathematical biology: Mathematics was key tocracking the genetic code. Now, new mathematics is needed to understand the three-dimensional structure of the proteins produced from that code. Celestial mechanics and cosmology: New methods have revealed a multitude of solutions to the three-body problem. And other new work may answer one of cosmology'smost fundamental questions: What is the size and shape of the universe? Mathematics and Everyday Life Traffic jams: New models are helping researchers understand where traffic jams come from-and maybe what to do about them! Small worlds: Researchers have found a short distance from theory to applications in the study of small world networks. Elegance in Mathematics Beyond Fermat's Last Theorem: Number theorists are reaching higher ground after Wiles' astounding 1994 proof: new developments inthe elegant world of elliptic curves and modular functions. The Millennium Prize Problems: The Clay Mathematics Institute has offered a million dollars for solutions to seven important and difficult unsolved problems. These are just some of the topics of current interest that are covered in thislatest volume of What's Happening in the Mathematical Sciences. The book has broad appeal for a wide spectrum of mathematicians and scientists, from high school students through advanced-level graduates and researchers.