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| four dimensional mathematical model of the universe: A Wrinkle in Time Madeleine L'Engle, 2010-04-01 NEWBERY MEDAL WINNER • TIME MAGAZINE’S 100 BEST FANTASY BOOKS OF ALL TIME • NOW A MAJOR MOTION PICTURE FROM DISNEY Read the ground-breaking science fiction and fantasy classic that has delighted children for over 60 years! A Wrinkle in Time is one of my favorite books of all time. I've read it so often, I know it by heart. —Meg Cabot Late one night, three otherworldly creatures appear and sweep Meg Murry, her brother Charles Wallace, and their friend Calvin O'Keefe away on a mission to save Mr. Murray, who has gone missing while doing top-secret work for the government. They travel via tesseract--a wrinkle that transports one across space and time--to the planet Camazotz, where Mr. Murray is being held captive. There they discover a dark force that threatens not only Mr. Murray but the safety of the whole universe. A Wrinkle in Time is the first book in Madeleine L’Engle’s Time Quintet. |
| four dimensional mathematical model of the universe: Geometry, Relativity and the Fourth Dimension Rudolf Rucker, 2012-06-08 Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Includes 141 illustrations. |
| four dimensional mathematical model of the universe: Flatland Edwin A. Abbott, 2024-09-17 A book that combines science fiction, satire of Victorian society and politics, proving to be a great literary allegory. The illustrated world is populated by Squares, Triangles, Circles and Lines living in a two-dimensional universe, all strictly divided by class and gender. The narrator is precisely one of them, a Square. He will guide readers into his world by explaining the brilliant implications of two-dimensional life. Later, however, he will tell of his discovery of other, more geometrically complex universes such as the three-dimensional one, represented by his encounter with a Sphere. Thus begins a true journey of knowledge, which will lead him to that which can hardly be conceived by the mind. A unique book that has become a cult object by the scientific community and beyond. |
| four dimensional mathematical model of the universe: Things to Make and Do in the Fourth Dimension Matt Parker, 2014-12-02 A book from the stand-up mathematician that makes math fun again! Math is boring, says the mathematician and comedian Matt Parker. Part of the problem may be the way the subject is taught, but it's also true that we all, to a greater or lesser extent, find math difficult and counterintuitive. This counterintuitiveness is actually part of the point, argues Parker: the extraordinary thing about math is that it allows us to access logic and ideas beyond what our brains can instinctively do—through its logical tools we are able to reach beyond our innate abilities and grasp more and more abstract concepts. In the absorbing and exhilarating Things to Make and Do in the Fourth Dimension, Parker sets out to convince his readers to revisit the very math that put them off the subject as fourteen-year-olds. Starting with the foundations of math familiar from school (numbers, geometry, and algebra), he reveals how it is possible to climb all the way up to the topology and to four-dimensional shapes, and from there to infinity—and slightly beyond. Both playful and sophisticated, Things to Make and Do in the Fourth Dimension is filled with captivating games and puzzles, a buffet of optional hands-on activities that entices us to take pleasure in math that is normally only available to those studying at a university level. Things to Make and Do in the Fourth Dimension invites us to re-learn much of what we missed in school and, this time, to be utterly enthralled by it. |
| four dimensional mathematical model of the universe: The Fourth Dimension Rudy von Bitter Rucker, Rudy Rucker, 1985 A detailed description of what the fourth dimension would be like. |
| four dimensional mathematical model of the universe: The Fourth Dimension: Toward a Geometry of Higher Reality Rudy Rucker, 2014-09-17 One of the most talented contemporary authors of cutting-edge math and science books conducts a fascinating tour of a higher reality, the Fourth Dimension. Includes problems, puzzles, and 200 drawings. Informative and mind-dazzling. — Martin Gardner. |
| four dimensional mathematical model of the universe: The Shape of Inner Space Shing-Tung Yau, Steven J. Nadis, 2010-09-07 The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations. |
| four dimensional mathematical model of the universe: Our Mathematical Universe Max Tegmark, 2015-02-03 Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians. |
| four dimensional mathematical model of the universe: The Wild World of 4-Manifolds Alexandru Scorpan, 2005-05-10 What a wonderful book! I strongly recommend this book to anyone, especially graduate students, interested in getting a sense of 4-manifolds. --MAA Reviews The book gives an excellent overview of 4-manifolds, with many figures and historical notes. Graduate students, nonexperts, and experts alike will enjoy browsing through it. -- Robion C. Kirby, University of California, Berkeley This book offers a panorama of the topology of simply connected smooth manifolds of dimension four. Dimension four is unlike any other dimension; it is large enough to have room for wild things to happen, but small enough so that there is no room to undo the wildness. For example, only manifolds of dimension four can exhibit infinitely many distinct smooth structures. Indeed, their topology remains the least understood today. To put things in context, the book starts with a survey of higher dimensions and of topological 4-manifolds. In the second part, the main invariant of a 4-manifold--the intersection form--and its interaction with the topology of the manifold are investigated. In the third part, as an important source of examples, complex surfaces are reviewed. In the final fourth part of the book, gauge theory is presented; this differential-geometric method has brought to light how unwieldy smooth 4-manifolds truly are, and while bringing new insights, has raised more questions than answers. The structure of the book is modular, organized into a main track of about two hundred pages, augmented by extensive notes at the end of each chapter, where many extra details, proofs and developments are presented. To help the reader, the text is peppered with over 250 illustrations and has an extensive index. |
| four dimensional mathematical model of the universe: Hyperspace Michio Kaku, 1994-03-24 Are there other dimensions beyond our own? Is time travel possible? Can we change the past? Are there gateways to parallel universes? All of us have pondered such questions, but there was a time when scientists dismissed these notions as outlandish speculations. Not any more. Today, they are the focus of the most intense scientific activity in recent memory. In Hyperspace, Michio Kaku, author of the widely acclaimed Beyond Einstein and a leading theoretical physicist, offers the first book-length tour of the most exciting (and perhaps most bizarre) work in modern physics, work which includes research on the tenth dimension, time warps, black holes, and multiple universes. The theory of hyperspace (or higher dimensional space)--and its newest wrinkle, superstring theory--stand at the center of this revolution, with adherents in every major research laboratory in the world, including several Nobel laureates. Beginning where Hawking's Brief History of Time left off, Kaku paints a vivid portrayal of the breakthroughs now rocking the physics establishment. Why all the excitement? As the author points out, for over half a century, scientists have puzzled over why the basic forces of the cosmos--gravity, electromagnetism, and the strong and weak nuclear forces--require markedly different mathematical descriptions. But if we see these forces as vibrations in a higher dimensional space, their field equations suddenly fit together like pieces in a jigsaw puzzle, perfectly snug, in an elegant, astonishingly simple form. This may thus be our leading candidate for the Theory of Everything. If so, it would be the crowning achievement of 2,000 years of scientific investigation into matter and its forces. Already, the theory has inspired several thousand research papers, and has been the focus of over 200 international conferences. Michio Kaku is one of the leading pioneers in superstring theory and has been at the forefront of this revolution in modern physics. With Hyperspace, he has produced a book for general readers which conveys the vitality of the field and the excitement as scientists grapple with the meaning of space and time. It is an exhilarating look at physics today and an eye-opening glimpse into the ultimate nature of the universe. |
| four dimensional mathematical model of the universe: A Visual Introduction to the Fourth Dimension (Rectangular 4D Geometry) Chris McMullen, Chris McMullen Ph D, 2013-01-19 This colorful, visual introduction to the fourth dimension provides a clear explanation of the concepts and numerous illustrations. It is written with a touch of personality that makes this an engaging read instead of a dry math text. The content is very accessible, yet at the same time detailed enough to satisfy the interests of advanced readers. This book is devoted to geometry; there are no spiritual or religious components to this book. May you enjoy your journey into the fascinating world of the fourth dimension! Contents: Introduction Chapter 0: What Is a Dimension? Chapter 1: Dimensions Zero and One Chapter 2: The Second Dimension Chapter 3: Three-Dimensional Space Chapter 4: A Fourth Dimension of Space Chapter 5: Tesseracts and Hypercubes Chapter 6: Hypercube Patterns Chapter 7: Planes and Hyperplanes Chapter 8: Tesseracts in Perspective Chapter 9: Rotations in 4D Space Chapter 10: Unfolding a Tesseract Chapter 11: Cross Sections of a Tesseract Chapter 12: Living in a 4D House Further Reading Glossary About the Author Put on your spacesuit, strap on your safety harness, swallow your anti-nausea medicine, and enjoy this journey into a fourth dimension of space! 10D, 9D, 8D, 7D, 6D, 5D, 4D, 3D, 2D, 1D, 0D. Blast off! |
| four dimensional mathematical model of the universe: Physics and Astrophysics Subal Kar, 2022-05-05 Physics and Astrophysics—Glimpses of the Progress provides a comprehensive account of physics and astrophysics from the time of Aristotle to the modern era of Stephen Hawking and beyond. It takes the readers of all ages through a pleasant journey touching on the major discoveries and inventions that have taken place in both the macro-world, including that in the cosmos, and the micro-world of atomic and subatomic particles related to physics and astrophysics. Use of historical perspective and anecdote makes the storytelling on the progress of physics and astrophysics both interesting and absorbing. While peering through different developments in these fields, the book never compromises with the sanctity of the scientific content, including the depth and beauty of the physical concept of the topics concerned and the philosophical viewpoints they represent. Where appropriate, the book also delves into value judgments of life that affect our civilization. Features The intricate concepts of physics and astrophysics are explained in simple terms and in easy-to-understand language. Physics and astrophysics are discussed in a connected and correlated way in a single volume of comprehensive size but in totality, which to date is the unique feature of this book. Starting with Aristotle’s Physics and going through the work of Newton, Einstein, Schrödinger, Hubble, Hewish, Hawking, and others, including the present research on dark energy, dark matter, and the fifth force of nature, the reader will be kept absorbed and spellbound. In addition to the fundamental principles of Newtonian mechanics, Einstein’s relativity, quantum mechanics, string theory, loop quantum gravity, and so on, the cutting-edge technologies of recent times, such as the Large Hadron Collider, Laser Interferometer Gravitational-wave Observatory, and Event Horizon Telescope, are also explored. The book is aimed primarily at undergraduate and graduate students, researchers, and professionals studying physics and astrophysics. General readers will also find the book useful to quench their thirst for knowledge about the developments in physics and astrophysics. |
| four dimensional mathematical model of the universe: Regular Polytopes H. S. M. Coxeter, 2012-05-23 Foremost book available on polytopes, incorporating ancient Greek and most modern work. Discusses polygons, polyhedrons, and multi-dimensional polytopes. Definitions of symbols. Includes 8 tables plus many diagrams and examples. 1963 edition. |
| four dimensional mathematical model of the universe: The Fourth Dimension and the Bible William Anthony Granville, 1922 |
| four dimensional mathematical model of the universe: Art Meets Mathematics in the Fourth Dimension Stephen Leon Lipscomb, 2014-10-13 To see objects that live in the fourth dimension we humans would need to add a fourth dimension to our three-dimensional vision. An example of such an object that lives in the fourth dimension is a hyper-sphere or “3-sphere.” The quest to imagine the elusive 3-sphere has deep historical roots: medieval poet Dante Alighieri used a 3-sphere to convey his allegorical vision of the Christian afterlife in his Divine Comedy. In 1917, Albert Einstein visualized the universe as a 3-sphere, describing this imagery as “the place where the reader’s imagination boggles. Nobody can imagine this thing.” Over time, however, understanding of the concept of a dimension evolved. By 2003, a researcher had successfully rendered into human vision the structure of a 4-web (think of an ever increasingly-dense spider’s web). In this text, Stephen Lipscomb takes his innovative dimension theory research a step further, using the 4-web to reveal a new partial image of a 3-sphere. Illustrations support the reader’s understanding of the mathematics behind this process. Lipscomb describes a computer program that can produce partial images of a 3-sphere and suggests methods of discerning other fourth-dimensional objects that may serve as the basis for future artwork. |
| four dimensional mathematical model of the universe: Relativity and the Dimensionality of the World Vesselin Petkov, 2009-09-03 The main focus of this volume is the question: is spacetime nothing more than a mathematical space (which describes the evolution in time of the ordinary three-dimensional world) or is it a mathematical model of a real four-dimensional world with time entirely given as the fourth dimension? The book contains fourteen invited papers which either directly address the main question of the nature of spacetime or explore issues related to it. |
| four dimensional mathematical model of the universe: Knots, Molecules, and the Universe Erica Flapan, 2015-12-22 This book is an elementary introduction to geometric topology and its applications to chemistry, molecular biology, and cosmology. It does not assume any mathematical or scientific background, sophistication, or even motivation to study mathematics. It is meant to be fun and engaging while drawing students in to learn about fundamental topological and geometric ideas. Though the book can be read and enjoyed by nonmathematicians, college students, or even eager high school students, it is intended to be used as an undergraduate textbook. The book is divided into three parts corresponding to the three areas referred to in the title. Part 1 develops techniques that enable two- and three-dimensional creatures to visualize possible shapes for their universe and to use topological and geometric properties to distinguish one such space from another. Part 2 is an introduction to knot theory with an emphasis on invariants. Part 3 presents applications of topology and geometry to molecular symmetries, DNA, and proteins. Each chapter ends with exercises that allow for better understanding of the material. The style of the book is informal and lively. Though all of the definitions and theorems are explicitly stated, they are given in an intuitive rather than a rigorous form, with several hundreds of figures illustrating the exposition. This allows students to develop intuition about topology and geometry without getting bogged down in technical details. |
| four dimensional mathematical model of the universe: The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory Brian Greene, 2003-09-30 Introduces the superstring theory that attempts to unite general relativity and quantum mechanics. |
| four dimensional mathematical model of the universe: The Planiverse A.K. Dewdney, 2012-12-06 A classic book about life in a two-dimensional universe, written by a well-known author. Now brought back into print in this revised and updated edition, the book is written within the great tradition of Abbott's Flatland, and Hinton's famous Sphereland. Accessible, imaginative, and clever, it will appeal to a wide array of readers, from serious mathematicians and computer scientists, to science fiction fans. |
| four dimensional mathematical model of the universe: Data Science Ivo D. Dinov, Milen Velchev Velev, 2021-12-06 The amount of new information is constantly increasing, faster than our ability to fully interpret and utilize it to improve human experiences. Addressing this asymmetry requires novel and revolutionary scientific methods and effective human and artificial intelligence interfaces. By lifting the concept of time from a positive real number to a 2D complex time (kime), this book uncovers a connection between artificial intelligence (AI), data science, and quantum mechanics. It proposes a new mathematical foundation for data science based on raising the 4D spacetime to a higher dimension where longitudinal data (e.g., time-series) are represented as manifolds (e.g., kime-surfaces). This new framework enables the development of innovative data science analytical methods for model-based and model-free scientific inference, derived computed phenotyping, and statistical forecasting. The book provides a transdisciplinary bridge and a pragmatic mechanism to translate quantum mechanical principles, such as particles and wavefunctions, into data science concepts, such as datum and inference-functions. It includes many open mathematical problems that still need to be solved, technological challenges that need to be tackled, and computational statistics algorithms that have to be fully developed and validated. Spacekime analytics provide mechanisms to effectively handle, process, and interpret large, heterogeneous, and continuously-tracked digital information from multiple sources. The authors propose computational methods, probability model-based techniques, and analytical strategies to estimate, approximate, or simulate the complex time phases (kime directions). This allows transforming time-varying data, such as time-series observations, into higher-dimensional manifolds representing complex-valued and kime-indexed surfaces (kime-surfaces). The book includes many illustrations of model-based and model-free spacekime analytic techniques applied to economic forecasting, identification of functional brain activation, and high-dimensional cohort phenotyping. Specific case-study examples include unsupervised clustering using the Michigan Consumer Sentiment Index (MCSI), model-based inference using functional magnetic resonance imaging (fMRI) data, and model-free inference using the UK Biobank data archive. The material includes mathematical, inferential, computational, and philosophical topics such as Heisenberg uncertainty principle and alternative approaches to large sample theory, where a few spacetime observations can be amplified by a series of derived, estimated, or simulated kime-phases. The authors extend Newton-Leibniz calculus of integration and differentiation to the spacekime manifold and discuss possible solutions to some of the problems of time. The coverage also includes 5D spacekime formulations of classical 4D spacetime mathematical equations describing natural laws of physics, as well as, statistical articulation of spacekime analytics in a Bayesian inference framework. The steady increase of the volume and complexity of observed and recorded digital information drives the urgent need to develop novel data analytical strategies. Spacekime analytics represents one new data-analytic approach, which provides a mechanism to understand compound phenomena that are observed as multiplex longitudinal processes and computationally tracked by proxy measures. This book may be of interest to academic scholars, graduate students, postdoctoral fellows, artificial intelligence and machine learning engineers, biostatisticians, econometricians, and data analysts. Some of the material may also resonate with philosophers, futurists, astrophysicists, space industry technicians, biomedical researchers, health practitioners, and the general public. |
| four dimensional mathematical model of the universe: The Science of Interstellar Kip Thorne, 2014-11-07 A journey through the otherworldly science behind Christopher Nolan’s award-winning film, Interstellar, from executive producer and Nobel Prize-winning physicist Kip Thorne. Interstellar, from acclaimed filmmaker Christopher Nolan, takes us on a fantastic voyage far beyond our solar system. Yet in The Science of Interstellar, Kip Thorne, the Nobel prize-winning physicist who assisted Nolan on the scientific aspects of Interstellar, shows us that the movie’s jaw-dropping events and stunning, never-before-attempted visuals are grounded in real science. Thorne shares his experiences working as the science adviser on the film and then moves on to the science itself. In chapters on wormholes, black holes, interstellar travel, and much more, Thorne’s scientific insights—many of them triggered during the actual scripting and shooting of Interstellar—describe the physical laws that govern our universe and the truly astounding phenomena that those laws make possible. Interstellar and all related characters and elements are trademarks of and © Warner Bros. Entertainment Inc. (s14). |
| four dimensional mathematical model of the universe: A Primer of Higher Space (the Fourth Dimension) Claude Fayette Bragdon, 1913 |
| four dimensional mathematical model of the universe: Theory And Phenomenology Of Sparticles: An Account Of Four-dimensional N=1 Supersymmetry In High Energy Physics Manuel Drees, Rohini Godbole, Probir Roy, 2005-01-18 Supersymmetry or SUSY, one of the most beautiful recent ideas of physics, predicts sparticles existing as superpartners of particles. This book gives a theoretical and phenomenological account of sparticles. Starting from a basic level, it provides a comprehensive, pedagogical and user-friendly treatment of the subject of four-dimensional N=1 supersymmetry as well as its observational aspects in high energy physics and cosmology. Part One of the book introduces the requisite formal theory, preceded by a discussion of the naturalness problem. Part Two describes the supersymmetrization of the Standard Model of particle interactions as well as the origin of soft supersymmetry breaking and how it can be mediated from higher energies. Search strategies for sparticles, supersymmetric Higgs bosons, nonminimal scenarios and cosmological implications are some of the other topics covered. Novel features of the book include a dictionary between two-component and four-component spinor notation, a step-by-step derivation of the nonrenormalization theorem, an extended discussion of supersymmetric renormalization group evolution, detailed analyses of minimal and nonminimal models with gravity (including anomaly) mediated and gauge mediated supersymmetry breaking as well as elaborate self-contained presentations of collider signals of sparticles plus supersymmetric Higgs bosons and of supersymmetric cosmology. Appendices list all Feynman rules for the vertices of the Minimal Supersymmetric Standard Model. |
| four dimensional mathematical model of the universe: Sphereland Dionys Burger, 1983 |
| four dimensional mathematical model of the universe: The Knot Book Colin Conrad Adams, 2004 Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics. |
| four dimensional mathematical model of the universe: Warped Passages Lisa Randall, 2009-10-21 The universe has many secrets. It may hide additional dimensions of space other than the familier three we recognize. There might even be another universe adjacent to ours, invisible and unattainable . . . for now. Warped Passages is a brilliantly readable and altogether exhilarating journey that tracks the arc of discovery from early twentieth-century physics to the razor's edge of modern scientific theory. One of the world's leading theoretical physicists, Lisa Randall provides astonishing scientific possibilities that, until recently, were restricted to the realm of science fiction. Unraveling the twisted threads of the most current debates on relativity, quantum mechanics, and gravity, she explores some of the most fundamental questions posed by Nature—taking us into the warped, hidden dimensions underpinning the universe we live in, demystifying the science of the myriad worlds that may exist just beyond our own. |
| four dimensional mathematical model of the universe: The Poincare Conjecture Donal O'Shea, 2009-05-26 Henri Poincaré was one of the greatest mathematicians of the late nineteenth and early twentieth century. He revolutionized the field of topology, which studies properties of geometric configurations that are unchanged by stretching or twisting. The Poincaré conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape of the universe. The conjecture states that there is only one shape possible for a finite universe in which every loop can be contracted to a single point. Poincaré's conjecture is one of the seven millennium problems that bring a one-million-dollar award for a solution. Grigory Perelman, a Russian mathematician, has offered a proof that is likely to win the Fields Medal, the mathematical equivalent of a Nobel prize, in August 2006. He also will almost certainly share a Clay Institute millennium award. In telling the vibrant story of The Poincaré Conjecture, Donal O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians whose work have led to Perelman's proof of this famous conjecture. |
| four dimensional mathematical model of the universe: Our Mathematical Universe Max Tegmark, 2014-01-07 Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians. |
| four dimensional mathematical model of the universe: Mathematical Models In Science Olav Arnfinn Laudal, 2021-06-16 Mathematical Models in Science treats General Relativity and Quantum Mechanics in a non-commutative Algebraic Geometric framework.Based on ideas first published in Geometry of Time-Spaces: Non-commutative Algebraic Geometry Applied to Quantum Theory (World Scientific, 2011), Olav Arnfinn Laudal proposes a Toy Model as a Theory of Everything, starting with the notion of the Big Bang in Cosmology, modeled as the non-commutative deformation of a thick point. From this point, the author shows how to extract reasonable models for both General Relativity and Quantum Theory. This book concludes that the universe turns out to be the 6-dimensional Hilbert scheme of pairs of points in affine 3-space. With this in place, one may develop within the model much of the physics known to the reader. In particular, this theory is applicable to the concept of Dark Matter and its effects on our visual universe.Hence, Mathematical Models in Science proves the dependency of deformation theory in Mathematical Physics and summarizes the development of physical applications of pure mathematics developed in the twentieth century. |
| four dimensional mathematical model of the universe: The Shape of a Life Shing-Tung Yau, Steve Nadis, 2019-02-19 A Fields medalist recounts his lifelong effort to uncover the geometric shape—the Calabi-Yau manifold—that may store the hidden dimensions of our universe. Harvard geometer Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics. “The remarkable story of one of the world’s most accomplished mathematicians . . . Yau’s personal journey—from escaping China as a youngster, leading a gang outside Hong Kong, becoming captivated by mathematics, to making breakthroughs that thrust him on the world stage—inspires us all with humankind’s irrepressible spirit of discovery.” —Brian Greene, New York Times–bestselling author of The Elegant Universe “An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.” —The Boston Globe “Engaging, eminently readable. . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.” —American Scientist |
| four dimensional mathematical model of the universe: The Expanding Worlds of General Relativity Hubert Goenner, Jürgen Renn, Jim Ritter, Tilman Sauer, 1998-12-01 The past decade has seen a considerable surge of interest in historical and philo sophical studies of gravitation and relativity, due not only to the tremendous amount of world-wide research in general relativity and its theoretical and observational consequences, but also to an increasing awareness that a collaboration between working scientists, historians and philosophers of science is, in this field, partic ularly promising for all participants. The expanding activity in this field is well documented by recent volumes in this Einstein Studies series on the History of General Relativity as well as by a series of international conferences on this topic at Osgood Hill (1986), Luminy (1988), and Pittsburgh (1991). The fourth of these conferences, hosted by the Max Planck Institute for the History of Science, was held in Berlin from 31 July to 3 August 1995, with a record attendance of some 80 historians and philosophers of science, physicists, mathematicians, and as tronomers. Based on presentations at the Berlin conference, this volume provides an overview of the present state of research in this field, documenting not only the increasing scope of recent investigations in the history of relativity and gravitation but also the emergence of several key issues that will probably remain at the focus of debate in the near future. RELATIVITY IN THE MAKING The papers of this section deal with the origins and genesis of relativity theory. |
| four dimensional mathematical model of the universe: Visualizing Mathematics with 3D Printing Henry Segerman, 2016-10-04 The first book to explain mathematics using 3D printed models. Winner of the Technical Text of the Washington Publishers Wouldn’t it be great to experience three-dimensional ideas in three dimensions? In this book—the first of its kind—mathematician and mathematical artist Henry Segerman takes readers on a fascinating tour of two-, three-, and four-dimensional mathematics, exploring Euclidean and non-Euclidean geometries, symmetry, knots, tilings, and soap films. Visualizing Mathematics with 3D Printing includes more than 100 color photographs of 3D printed models. Readers can take the book’s insights to a new level by visiting its sister website, 3dprintmath.com, which features virtual three-dimensional versions of the models for readers to explore. These models can also be ordered online or downloaded to print on a 3D printer. Combining the strengths of book and website, this volume pulls higher geometry and topology out of the realm of the abstract and puts it into the hands of anyone fascinated by mathematical relationships of shape. With the book in one hand and a 3D printed model in the other, readers can find deeper meaning while holding a hyperbolic honeycomb, touching the twists of a torus knot, or caressing the curves of a Klein quartic. |
| four dimensional mathematical model of the universe: Exploring the Fourth Dimension John D. Ralphs, 1992 |
| four dimensional mathematical model of the universe: The Tenseless Theory of Time W.L. Craig, 2013-03-09 he present book and its companion volume The Tensed Theory of Time: a T Critical Examination are an attempt to adjudicate what one recent discussant has called the most fundamental question in the philosophy of time, namely, whether a static or a dynamic conception ofthe world is correct. ] I had originally intended to treat this question in the space of a single volume; but the study swelled into two. I found that an adequate appraisal of these two competing theories of time requires a wide-ranging discussion of issues in metaphysics, philosophy of language, phenomenology, philosophy of science, philosophy of space and time, and even philosophy of religion, and that this simply could not be done in one volume. If these volumes succeed in making a contribution to the debate, it will be precisely because of the synoptic nature of the discussion therein. Too often the question of the nature of time has been prematurely answered by some philosopher or physicist simply because he is largely ignorant of relevant discussions outside his chosen field of expertise. In these two complementary but independent volumes I have attempted to appraise what I take to be the most important arguments drawn from a variety of fields for and against each theory of time. |
| four dimensional mathematical model of the universe: Time, Space, Stars & Man Michael Mark Woolfson, M. M. Woolfson, 2013 The three greatest scientific mysteries, which remain poorly understood, are the origin of the universe, the origin of life and the development of consciousness. This book describes the processes preceding the Big Bang, the creation of matter, the concentration of that matter into stars and planets, the development of simple life forms and the theory of evolution that has given higher life forms, including mankind.There are many popular and excellent science books that present various aspects of science. However, this book follows a narrow scientific pathway from the Big Bang to mankind, and depicts the causal relationship between each step and the next. The science covered will be enough to satisfy most readers. Many important areas of science are dealt with, and these include cosmology, particle physics, atomic physics, galaxy and star formation, planet formation and aspects of evolution. The necessary science is described in a narrative form that general-interest readers should understand, without the use of equations or formulae.This 2nd edition includes several updates on the subjects that form the pillars of this book. They are: cosmology and astronomy, the features and formation of the solar system, the origin of life, and genetics and evolution. This book will appeal to readers with an interest in biology and those curious about the origins of the universe. |
| four dimensional mathematical model of the universe: Relativity and the Nature of Spacetime Vesselin Petkov, 2009-06-23 Puts the emphasis on conceptual questions: Why is there no such thing as absolute motion? What is the physical meaning of relativity of simultaneity? But, the most important question that is addressed in this book is what is the nature of spacetime? or, equivalently, what is the dimensionality of the world at the macroscopic level? Develops answers to these questions via a thorough analysis of relativistic effects and explicitly asking whether the objects involved in those effects are three-dimensional or four-dimensional. Discusses the implication of the result (this analysis clearly shows that if the world and the physical objects were three-dimensional, none of the kinematic relativistic effects and the experimental evidence supporting them would be possible) for physics, philosophy, and our entire world view are discussed. |
| four dimensional mathematical model of the universe: Advanced Remote Sensing Technology for Tsunami Modelling and Forecasting Maged Marghany, 2018-07-04 The innovation in space technologies has generated a new method for observing and monitoring tsunamis from space. Most tsunami remote sensing studies focus on using classical image processing tools or conventional edge detection procedures. However, these methods do not use modern physics, applied mathematics, signal communication, remote sensing data and innovative space technologies. This book equips readers to understand how to monitor tsunamis from space with remote sensing technology art to create a better alarm warning system. |
| four dimensional mathematical model of the universe: Fiction Refracts Science Allen Thiher, 2005 Examines the relationship between science and the fiction developed by modernists, including Musil, Proust, Kafka, and Joyce. Looks at Pascalian and Newtonian cosmology, Darwinism, epistemology, relativity theory, quantum mechanics, the development of modernist and postmodern fiction, positivism, and finally works by Woolf, Faulkner, and Borges--Provided by publisher. |
| four dimensional mathematical model of the universe: Archimedes to Hawking Clifford Pickover, 2008-04-16 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. |
| four dimensional mathematical model of the universe: Introduction to Tensor Analysis and the Calculus of Moving Surfaces Pavel Grinfeld, 2013-09-24 This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations. The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author’s skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 – when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject. The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem. |
| four-dimensional mathematical model of the universe: A Wrinkle in Time Madeleine L'Engle, 2010-04-01 NEWBERY MEDAL WINNER • TIME MAGAZINE’S 100 BEST FANTASY BOOKS OF ALL TIME • NOW A MAJOR MOTION PICTURE FROM DISNEY Read the ground-breaking science fiction and fantasy classic that has delighted children for over 60 years! A Wrinkle in Time is one of my favorite books of all time. I've read it so often, I know it by heart. —Meg Cabot Late one night, three otherworldly creatures appear and sweep Meg Murry, her brother Charles Wallace, and their friend Calvin O'Keefe away on a mission to save Mr. Murray, who has gone missing while doing top-secret work for the government. They travel via tesseract--a wrinkle that transports one across space and time--to the planet Camazotz, where Mr. Murray is being held captive. There they discover a dark force that threatens not only Mr. Murray but the safety of the whole universe. A Wrinkle in Time is the first book in Madeleine L’Engle’s Time Quintet. |
| four-dimensional mathematical model of the universe: Geometry, Relativity and the Fourth Dimension Rudolf Rucker, 2012-06-08 Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Includes 141 illustrations. |
| four-dimensional mathematical model of the universe: Flatland Edwin A. Abbott, 2024-09-17 A book that combines science fiction, satire of Victorian society and politics, proving to be a great literary allegory. The illustrated world is populated by Squares, Triangles, Circles and Lines living in a two-dimensional universe, all strictly divided by class and gender. The narrator is precisely one of them, a Square. He will guide readers into his world by explaining the brilliant implications of two-dimensional life. Later, however, he will tell of his discovery of other, more geometrically complex universes such as the three-dimensional one, represented by his encounter with a Sphere. Thus begins a true journey of knowledge, which will lead him to that which can hardly be conceived by the mind. A unique book that has become a cult object by the scientific community and beyond. |
| four-dimensional mathematical model of the universe: Things to Make and Do in the Fourth Dimension Matt Parker, 2014-12-02 A book from the stand-up mathematician that makes math fun again! Math is boring, says the mathematician and comedian Matt Parker. Part of the problem may be the way the subject is taught, but it's also true that we all, to a greater or lesser extent, find math difficult and counterintuitive. This counterintuitiveness is actually part of the point, argues Parker: the extraordinary thing about math is that it allows us to access logic and ideas beyond what our brains can instinctively do—through its logical tools we are able to reach beyond our innate abilities and grasp more and more abstract concepts. In the absorbing and exhilarating Things to Make and Do in the Fourth Dimension, Parker sets out to convince his readers to revisit the very math that put them off the subject as fourteen-year-olds. Starting with the foundations of math familiar from school (numbers, geometry, and algebra), he reveals how it is possible to climb all the way up to the topology and to four-dimensional shapes, and from there to infinity—and slightly beyond. Both playful and sophisticated, Things to Make and Do in the Fourth Dimension is filled with captivating games and puzzles, a buffet of optional hands-on activities that entices us to take pleasure in math that is normally only available to those studying at a university level. Things to Make and Do in the Fourth Dimension invites us to re-learn much of what we missed in school and, this time, to be utterly enthralled by it. |
| four-dimensional mathematical model of the universe: The Fourth Dimension Rudy von Bitter Rucker, Rudy Rucker, 1985 A detailed description of what the fourth dimension would be like. |
| four-dimensional mathematical model of the universe: The Fourth Dimension: Toward a Geometry of Higher Reality Rudy Rucker, 2014-09-17 One of the most talented contemporary authors of cutting-edge math and science books conducts a fascinating tour of a higher reality, the Fourth Dimension. Includes problems, puzzles, and 200 drawings. Informative and mind-dazzling. — Martin Gardner. |
| four-dimensional mathematical model of the universe: The Wild World of 4-Manifolds Alexandru Scorpan, 2005-05-10 What a wonderful book! I strongly recommend this book to anyone, especially graduate students, interested in getting a sense of 4-manifolds. --MAA Reviews The book gives an excellent overview of 4-manifolds, with many figures and historical notes. Graduate students, nonexperts, and experts alike will enjoy browsing through it. -- Robion C. Kirby, University of California, Berkeley This book offers a panorama of the topology of simply connected smooth manifolds of dimension four. Dimension four is unlike any other dimension; it is large enough to have room for wild things to happen, but small enough so that there is no room to undo the wildness. For example, only manifolds of dimension four can exhibit infinitely many distinct smooth structures. Indeed, their topology remains the least understood today. To put things in context, the book starts with a survey of higher dimensions and of topological 4-manifolds. In the second part, the main invariant of a 4-manifold--the intersection form--and its interaction with the topology of the manifold are investigated. In the third part, as an important source of examples, complex surfaces are reviewed. In the final fourth part of the book, gauge theory is presented; this differential-geometric method has brought to light how unwieldy smooth 4-manifolds truly are, and while bringing new insights, has raised more questions than answers. The structure of the book is modular, organized into a main track of about two hundred pages, augmented by extensive notes at the end of each chapter, where many extra details, proofs and developments are presented. To help the reader, the text is peppered with over 250 illustrations and has an extensive index. |
| four-dimensional mathematical model of the universe: Our Mathematical Universe Max Tegmark, 2015-02-03 Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians. |
| four-dimensional mathematical model of the universe: The Shape of Inner Space Shing-Tung Yau, Steven J. Nadis, 2010-09-07 The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations. |
| four-dimensional mathematical model of the universe: Hyperspace Michio Kaku, 1994-03-24 Are there other dimensions beyond our own? Is time travel possible? Can we change the past? Are there gateways to parallel universes? All of us have pondered such questions, but there was a time when scientists dismissed these notions as outlandish speculations. Not any more. Today, they are the focus of the most intense scientific activity in recent memory. In Hyperspace, Michio Kaku, author of the widely acclaimed Beyond Einstein and a leading theoretical physicist, offers the first book-length tour of the most exciting (and perhaps most bizarre) work in modern physics, work which includes research on the tenth dimension, time warps, black holes, and multiple universes. The theory of hyperspace (or higher dimensional space)--and its newest wrinkle, superstring theory--stand at the center of this revolution, with adherents in every major research laboratory in the world, including several Nobel laureates. Beginning where Hawking's Brief History of Time left off, Kaku paints a vivid portrayal of the breakthroughs now rocking the physics establishment. Why all the excitement? As the author points out, for over half a century, scientists have puzzled over why the basic forces of the cosmos--gravity, electromagnetism, and the strong and weak nuclear forces--require markedly different mathematical descriptions. But if we see these forces as vibrations in a higher dimensional space, their field equations suddenly fit together like pieces in a jigsaw puzzle, perfectly snug, in an elegant, astonishingly simple form. This may thus be our leading candidate for the Theory of Everything. If so, it would be the crowning achievement of 2,000 years of scientific investigation into matter and its forces. Already, the theory has inspired several thousand research papers, and has been the focus of over 200 international conferences. Michio Kaku is one of the leading pioneers in superstring theory and has been at the forefront of this revolution in modern physics. With Hyperspace, he has produced a book for general readers which conveys the vitality of the field and the excitement as scientists grapple with the meaning of space and time. It is an exhilarating look at physics today and an eye-opening glimpse into the ultimate nature of the universe. |
| four-dimensional mathematical model of the universe: A Visual Introduction to the Fourth Dimension (Rectangular 4D Geometry) Chris McMullen, Chris McMullen Ph D, 2013-01-19 This colorful, visual introduction to the fourth dimension provides a clear explanation of the concepts and numerous illustrations. It is written with a touch of personality that makes this an engaging read instead of a dry math text. The content is very accessible, yet at the same time detailed enough to satisfy the interests of advanced readers. This book is devoted to geometry; there are no spiritual or religious components to this book. May you enjoy your journey into the fascinating world of the fourth dimension! Contents: Introduction Chapter 0: What Is a Dimension? Chapter 1: Dimensions Zero and One Chapter 2: The Second Dimension Chapter 3: Three-Dimensional Space Chapter 4: A Fourth Dimension of Space Chapter 5: Tesseracts and Hypercubes Chapter 6: Hypercube Patterns Chapter 7: Planes and Hyperplanes Chapter 8: Tesseracts in Perspective Chapter 9: Rotations in 4D Space Chapter 10: Unfolding a Tesseract Chapter 11: Cross Sections of a Tesseract Chapter 12: Living in a 4D House Further Reading Glossary About the Author Put on your spacesuit, strap on your safety harness, swallow your anti-nausea medicine, and enjoy this journey into a fourth dimension of space! 10D, 9D, 8D, 7D, 6D, 5D, 4D, 3D, 2D, 1D, 0D. Blast off! |
| four-dimensional mathematical model of the universe: Regular Polytopes H. S. M. Coxeter, 2012-05-23 Foremost book available on polytopes, incorporating ancient Greek and most modern work. Discusses polygons, polyhedrons, and multi-dimensional polytopes. Definitions of symbols. Includes 8 tables plus many diagrams and examples. 1963 edition. |
| four-dimensional mathematical model of the universe: Physics and Astrophysics Subal Kar, 2022-05-05 Physics and Astrophysics—Glimpses of the Progress provides a comprehensive account of physics and astrophysics from the time of Aristotle to the modern era of Stephen Hawking and beyond. It takes the readers of all ages through a pleasant journey touching on the major discoveries and inventions that have taken place in both the macro-world, including that in the cosmos, and the micro-world of atomic and subatomic particles related to physics and astrophysics. Use of historical perspective and anecdote makes the storytelling on the progress of physics and astrophysics both interesting and absorbing. While peering through different developments in these fields, the book never compromises with the sanctity of the scientific content, including the depth and beauty of the physical concept of the topics concerned and the philosophical viewpoints they represent. Where appropriate, the book also delves into value judgments of life that affect our civilization. Features The intricate concepts of physics and astrophysics are explained in simple terms and in easy-to-understand language. Physics and astrophysics are discussed in a connected and correlated way in a single volume of comprehensive size but in totality, which to date is the unique feature of this book. Starting with Aristotle’s Physics and going through the work of Newton, Einstein, Schrödinger, Hubble, Hewish, Hawking, and others, including the present research on dark energy, dark matter, and the fifth force of nature, the reader will be kept absorbed and spellbound. In addition to the fundamental principles of Newtonian mechanics, Einstein’s relativity, quantum mechanics, string theory, loop quantum gravity, and so on, the cutting-edge technologies of recent times, such as the Large Hadron Collider, Laser Interferometer Gravitational-wave Observatory, and Event Horizon Telescope, are also explored. The book is aimed primarily at undergraduate and graduate students, researchers, and professionals studying physics and astrophysics. General readers will also find the book useful to quench their thirst for knowledge about the developments in physics and astrophysics. |
| four-dimensional mathematical model of the universe: Relativity and the Dimensionality of the World Vesselin Petkov, 2009-09-03 The main focus of this volume is the question: is spacetime nothing more than a mathematical space (which describes the evolution in time of the ordinary three-dimensional world) or is it a mathematical model of a real four-dimensional world with time entirely given as the fourth dimension? The book contains fourteen invited papers which either directly address the main question of the nature of spacetime or explore issues related to it. |
| four-dimensional mathematical model of the universe: Art Meets Mathematics in the Fourth Dimension Stephen Leon Lipscomb, 2014-10-13 To see objects that live in the fourth dimension we humans would need to add a fourth dimension to our three-dimensional vision. An example of such an object that lives in the fourth dimension is a hyper-sphere or “3-sphere.” The quest to imagine the elusive 3-sphere has deep historical roots: medieval poet Dante Alighieri used a 3-sphere to convey his allegorical vision of the Christian afterlife in his Divine Comedy. In 1917, Albert Einstein visualized the universe as a 3-sphere, describing this imagery as “the place where the reader’s imagination boggles. Nobody can imagine this thing.” Over time, however, understanding of the concept of a dimension evolved. By 2003, a researcher had successfully rendered into human vision the structure of a 4-web (think of an ever increasingly-dense spider’s web). In this text, Stephen Lipscomb takes his innovative dimension theory research a step further, using the 4-web to reveal a new partial image of a 3-sphere. Illustrations support the reader’s understanding of the mathematics behind this process. Lipscomb describes a computer program that can produce partial images of a 3-sphere and suggests methods of discerning other fourth-dimensional objects that may serve as the basis for future artwork. |
| four-dimensional mathematical model of the universe: The Fourth Dimension and the Bible William Anthony Granville, 1922 |
| four-dimensional mathematical model of the universe: Knots, Molecules, and the Universe Erica Flapan, 2015-12-22 This book is an elementary introduction to geometric topology and its applications to chemistry, molecular biology, and cosmology. It does not assume any mathematical or scientific background, sophistication, or even motivation to study mathematics. It is meant to be fun and engaging while drawing students in to learn about fundamental topological and geometric ideas. Though the book can be read and enjoyed by nonmathematicians, college students, or even eager high school students, it is intended to be used as an undergraduate textbook. The book is divided into three parts corresponding to the three areas referred to in the title. Part 1 develops techniques that enable two- and three-dimensional creatures to visualize possible shapes for their universe and to use topological and geometric properties to distinguish one such space from another. Part 2 is an introduction to knot theory with an emphasis on invariants. Part 3 presents applications of topology and geometry to molecular symmetries, DNA, and proteins. Each chapter ends with exercises that allow for better understanding of the material. The style of the book is informal and lively. Though all of the definitions and theorems are explicitly stated, they are given in an intuitive rather than a rigorous form, with several hundreds of figures illustrating the exposition. This allows students to develop intuition about topology and geometry without getting bogged down in technical details. |
| four-dimensional mathematical model of the universe: The Planiverse A.K. Dewdney, 2012-12-06 A classic book about life in a two-dimensional universe, written by a well-known author. Now brought back into print in this revised and updated edition, the book is written within the great tradition of Abbott's Flatland, and Hinton's famous Sphereland. Accessible, imaginative, and clever, it will appeal to a wide array of readers, from serious mathematicians and computer scientists, to science fiction fans. |
| four-dimensional mathematical model of the universe: Data Science Ivo D. Dinov, Milen Velchev Velev, 2021-12-06 The amount of new information is constantly increasing, faster than our ability to fully interpret and utilize it to improve human experiences. Addressing this asymmetry requires novel and revolutionary scientific methods and effective human and artificial intelligence interfaces. By lifting the concept of time from a positive real number to a 2D complex time (kime), this book uncovers a connection between artificial intelligence (AI), data science, and quantum mechanics. It proposes a new mathematical foundation for data science based on raising the 4D spacetime to a higher dimension where longitudinal data (e.g., time-series) are represented as manifolds (e.g., kime-surfaces). This new framework enables the development of innovative data science analytical methods for model-based and model-free scientific inference, derived computed phenotyping, and statistical forecasting. The book provides a transdisciplinary bridge and a pragmatic mechanism to translate quantum mechanical principles, such as particles and wavefunctions, into data science concepts, such as datum and inference-functions. It includes many open mathematical problems that still need to be solved, technological challenges that need to be tackled, and computational statistics algorithms that have to be fully developed and validated. Spacekime analytics provide mechanisms to effectively handle, process, and interpret large, heterogeneous, and continuously-tracked digital information from multiple sources. The authors propose computational methods, probability model-based techniques, and analytical strategies to estimate, approximate, or simulate the complex time phases (kime directions). This allows transforming time-varying data, such as time-series observations, into higher-dimensional manifolds representing complex-valued and kime-indexed surfaces (kime-surfaces). The book includes many illustrations of model-based and model-free spacekime analytic techniques applied to economic forecasting, identification of functional brain activation, and high-dimensional cohort phenotyping. Specific case-study examples include unsupervised clustering using the Michigan Consumer Sentiment Index (MCSI), model-based inference using functional magnetic resonance imaging (fMRI) data, and model-free inference using the UK Biobank data archive. The material includes mathematical, inferential, computational, and philosophical topics such as Heisenberg uncertainty principle and alternative approaches to large sample theory, where a few spacetime observations can be amplified by a series of derived, estimated, or simulated kime-phases. The authors extend Newton-Leibniz calculus of integration and differentiation to the spacekime manifold and discuss possible solutions to some of the problems of time. The coverage also includes 5D spacekime formulations of classical 4D spacetime mathematical equations describing natural laws of physics, as well as, statistical articulation of spacekime analytics in a Bayesian inference framework. The steady increase of the volume and complexity of observed and recorded digital information drives the urgent need to develop novel data analytical strategies. Spacekime analytics represents one new data-analytic approach, which provides a mechanism to understand compound phenomena that are observed as multiplex longitudinal processes and computationally tracked by proxy measures. This book may be of interest to academic scholars, graduate students, postdoctoral fellows, artificial intelligence and machine learning engineers, biostatisticians, econometricians, and data analysts. Some of the material may also resonate with philosophers, futurists, astrophysicists, space industry technicians, biomedical researchers, health practitioners, and the general public. |
| four-dimensional mathematical model of the universe: The Science of Interstellar Kip Thorne, 2014-11-07 A journey through the otherworldly science behind Christopher Nolan’s award-winning film, Interstellar, from executive producer and Nobel Prize-winning physicist Kip Thorne. Interstellar, from acclaimed filmmaker Christopher Nolan, takes us on a fantastic voyage far beyond our solar system. Yet in The Science of Interstellar, Kip Thorne, the Nobel prize-winning physicist who assisted Nolan on the scientific aspects of Interstellar, shows us that the movie’s jaw-dropping events and stunning, never-before-attempted visuals are grounded in real science. Thorne shares his experiences working as the science adviser on the film and then moves on to the science itself. In chapters on wormholes, black holes, interstellar travel, and much more, Thorne’s scientific insights—many of them triggered during the actual scripting and shooting of Interstellar—describe the physical laws that govern our universe and the truly astounding phenomena that those laws make possible. Interstellar and all related characters and elements are trademarks of and © Warner Bros. Entertainment Inc. (s14). |
| four-dimensional mathematical model of the universe: A Primer of Higher Space (the Fourth Dimension) Claude Fayette Bragdon, 1913 |
| four-dimensional mathematical model of the universe: Theory And Phenomenology Of Sparticles: An Account Of Four-dimensional N=1 Supersymmetry In High Energy Physics Manuel Drees, Rohini Godbole, Probir Roy, 2005-01-18 Supersymmetry or SUSY, one of the most beautiful recent ideas of physics, predicts sparticles existing as superpartners of particles. This book gives a theoretical and phenomenological account of sparticles. Starting from a basic level, it provides a comprehensive, pedagogical and user-friendly treatment of the subject of four-dimensional N=1 supersymmetry as well as its observational aspects in high energy physics and cosmology. Part One of the book introduces the requisite formal theory, preceded by a discussion of the naturalness problem. Part Two describes the supersymmetrization of the Standard Model of particle interactions as well as the origin of soft supersymmetry breaking and how it can be mediated from higher energies. Search strategies for sparticles, supersymmetric Higgs bosons, nonminimal scenarios and cosmological implications are some of the other topics covered. Novel features of the book include a dictionary between two-component and four-component spinor notation, a step-by-step derivation of the nonrenormalization theorem, an extended discussion of supersymmetric renormalization group evolution, detailed analyses of minimal and nonminimal models with gravity (including anomaly) mediated and gauge mediated supersymmetry breaking as well as elaborate self-contained presentations of collider signals of sparticles plus supersymmetric Higgs bosons and of supersymmetric cosmology. Appendices list all Feynman rules for the vertices of the Minimal Supersymmetric Standard Model. |
| four-dimensional mathematical model of the universe: Sphereland Dionys Burger, 1983 |
| four-dimensional mathematical model of the universe: The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory Brian Greene, 2003-09-30 Introduces the superstring theory that attempts to unite general relativity and quantum mechanics. |
| four-dimensional mathematical model of the universe: The Knot Book Colin Conrad Adams, 2004 Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics. |
| four-dimensional mathematical model of the universe: The Poincare Conjecture Donal O'Shea, 2009-05-26 Henri Poincaré was one of the greatest mathematicians of the late nineteenth and early twentieth century. He revolutionized the field of topology, which studies properties of geometric configurations that are unchanged by stretching or twisting. The Poincaré conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape of the universe. The conjecture states that there is only one shape possible for a finite universe in which every loop can be contracted to a single point. Poincaré's conjecture is one of the seven millennium problems that bring a one-million-dollar award for a solution. Grigory Perelman, a Russian mathematician, has offered a proof that is likely to win the Fields Medal, the mathematical equivalent of a Nobel prize, in August 2006. He also will almost certainly share a Clay Institute millennium award. In telling the vibrant story of The Poincaré Conjecture, Donal O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians whose work have led to Perelman's proof of this famous conjecture. |
| four-dimensional mathematical model of the universe: Mathematical Models In Science Olav Arnfinn Laudal, 2021-06-16 Mathematical Models in Science treats General Relativity and Quantum Mechanics in a non-commutative Algebraic Geometric framework.Based on ideas first published in Geometry of Time-Spaces: Non-commutative Algebraic Geometry Applied to Quantum Theory (World Scientific, 2011), Olav Arnfinn Laudal proposes a Toy Model as a Theory of Everything, starting with the notion of the Big Bang in Cosmology, modeled as the non-commutative deformation of a thick point. From this point, the author shows how to extract reasonable models for both General Relativity and Quantum Theory. This book concludes that the universe turns out to be the 6-dimensional Hilbert scheme of pairs of points in affine 3-space. With this in place, one may develop within the model much of the physics known to the reader. In particular, this theory is applicable to the concept of Dark Matter and its effects on our visual universe.Hence, Mathematical Models in Science proves the dependency of deformation theory in Mathematical Physics and summarizes the development of physical applications of pure mathematics developed in the twentieth century. |
| four-dimensional mathematical model of the universe: Our Mathematical Universe Max Tegmark, 2014-01-07 Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians. |
| four-dimensional mathematical model of the universe: Visualizing Mathematics with 3D Printing Henry Segerman, 2016-10-04 The first book to explain mathematics using 3D printed models. Winner of the Technical Text of the Washington Publishers Wouldn’t it be great to experience three-dimensional ideas in three dimensions? In this book—the first of its kind—mathematician and mathematical artist Henry Segerman takes readers on a fascinating tour of two-, three-, and four-dimensional mathematics, exploring Euclidean and non-Euclidean geometries, symmetry, knots, tilings, and soap films. Visualizing Mathematics with 3D Printing includes more than 100 color photographs of 3D printed models. Readers can take the book’s insights to a new level by visiting its sister website, 3dprintmath.com, which features virtual three-dimensional versions of the models for readers to explore. These models can also be ordered online or downloaded to print on a 3D printer. Combining the strengths of book and website, this volume pulls higher geometry and topology out of the realm of the abstract and puts it into the hands of anyone fascinated by mathematical relationships of shape. With the book in one hand and a 3D printed model in the other, readers can find deeper meaning while holding a hyperbolic honeycomb, touching the twists of a torus knot, or caressing the curves of a Klein quartic. |
| four-dimensional mathematical model of the universe: The Shape of a Life Shing-Tung Yau, Steve Nadis, 2019-02-19 A Fields medalist recounts his lifelong effort to uncover the geometric shape—the Calabi-Yau manifold—that may store the hidden dimensions of our universe. Harvard geometer Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics. “The remarkable story of one of the world’s most accomplished mathematicians . . . Yau’s personal journey—from escaping China as a youngster, leading a gang outside Hong Kong, becoming captivated by mathematics, to making breakthroughs that thrust him on the world stage—inspires us all with humankind’s irrepressible spirit of discovery.” —Brian Greene, New York Times–bestselling author of The Elegant Universe “An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.” —The Boston Globe “Engaging, eminently readable. . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.” —American Scientist |
| four-dimensional mathematical model of the universe: The Expanding Worlds of General Relativity Hubert Goenner, Jürgen Renn, Jim Ritter, Tilman Sauer, 1998-12-01 The past decade has seen a considerable surge of interest in historical and philo sophical studies of gravitation and relativity, due not only to the tremendous amount of world-wide research in general relativity and its theoretical and observational consequences, but also to an increasing awareness that a collaboration between working scientists, historians and philosophers of science is, in this field, partic ularly promising for all participants. The expanding activity in this field is well documented by recent volumes in this Einstein Studies series on the History of General Relativity as well as by a series of international conferences on this topic at Osgood Hill (1986), Luminy (1988), and Pittsburgh (1991). The fourth of these conferences, hosted by the Max Planck Institute for the History of Science, was held in Berlin from 31 July to 3 August 1995, with a record attendance of some 80 historians and philosophers of science, physicists, mathematicians, and as tronomers. Based on presentations at the Berlin conference, this volume provides an overview of the present state of research in this field, documenting not only the increasing scope of recent investigations in the history of relativity and gravitation but also the emergence of several key issues that will probably remain at the focus of debate in the near future. RELATIVITY IN THE MAKING The papers of this section deal with the origins and genesis of relativity theory. |
| four-dimensional mathematical model of the universe: Exploring the Fourth Dimension John D. Ralphs, 1992 |
| four-dimensional mathematical model of the universe: Time, Space, Stars & Man M. M. Woolfson, 2013 The three greatest scientific mysteries, which remain poorly understood, are the origin of the universe, the origin of life and the development of consciousness. This book describes the processes preceding the Big Bang, the creation of matter, the concentration of that matter into stars and planets, the development of simple life forms and the theory of evolution that has given higher life forms, including mankind.There are many popular and excellent science books that present various aspects of science. However, this book follows a narrow scientific pathway from the Big Bang to mankind, and depicts the causal relationship between each step and the next. The science covered will be enough to satisfy most readers. Many important areas of science are dealt with, and these include cosmology, particle physics, atomic physics, galaxy and star formation, planet formation and aspects of evolution. The necessary science is described in a narrative form that general-interest readers should understand, without the use of equations or formulae.This 2nd edition includes several updates on the subjects that form the pillars of this book. They are: cosmology and astronomy, the features and formation of the solar system, the origin of life, and genetics and evolution. This book will appeal to readers with an interest in biology and those curious about the origins of the universe. |
| four-dimensional mathematical model of the universe: Relativity and the Nature of Spacetime Vesselin Petkov, 2009-06-23 Puts the emphasis on conceptual questions: Why is there no such thing as absolute motion? What is the physical meaning of relativity of simultaneity? But, the most important question that is addressed in this book is what is the nature of spacetime? or, equivalently, what is the dimensionality of the world at the macroscopic level? Develops answers to these questions via a thorough analysis of relativistic effects and explicitly asking whether the objects involved in those effects are three-dimensional or four-dimensional. Discusses the implication of the result (this analysis clearly shows that if the world and the physical objects were three-dimensional, none of the kinematic relativistic effects and the experimental evidence supporting them would be possible) for physics, philosophy, and our entire world view are discussed. |
| four-dimensional mathematical model of the universe: Advanced Remote Sensing Technology for Tsunami Modelling and Forecasting Maged Marghany, 2018-07-04 The innovation in space technologies has generated a new method for observing and monitoring tsunamis from space. Most tsunami remote sensing studies focus on using classical image processing tools or conventional edge detection procedures. However, these methods do not use modern physics, applied mathematics, signal communication, remote sensing data and innovative space technologies. This book equips readers to understand how to monitor tsunamis from space with remote sensing technology art to create a better alarm warning system. |
| four-dimensional mathematical model of the universe: Fiction Refracts Science Allen Thiher, 2005 Examines the relationship between science and the fiction developed by modernists, including Musil, Proust, Kafka, and Joyce. Looks at Pascalian and Newtonian cosmology, Darwinism, epistemology, relativity theory, quantum mechanics, the development of modernist and postmodern fiction, positivism, and finally works by Woolf, Faulkner, and Borges--Provided by publisher. |
| four-dimensional mathematical model of the universe: Introduction to Tensor Analysis and the Calculus of Moving Surfaces Pavel Grinfeld, 2013-09-24 This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations. The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author’s skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 – when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject. The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem. |
| four-dimensional mathematical model of the universe: The Tenseless Theory of Time W.L. Craig, 2013-03-09 he present book and its companion volume The Tensed Theory of Time: a T Critical Examination are an attempt to adjudicate what one recent discussant has called the most fundamental question in the philosophy of time, namely, whether a static or a dynamic conception ofthe world is correct. ] I had originally intended to treat this question in the space of a single volume; but the study swelled into two. I found that an adequate appraisal of these two competing theories of time requires a wide-ranging discussion of issues in metaphysics, philosophy of language, phenomenology, philosophy of science, philosophy of space and time, and even philosophy of religion, and that this simply could not be done in one volume. If these volumes succeed in making a contribution to the debate, it will be precisely because of the synoptic nature of the discussion therein. Too often the question of the nature of time has been prematurely answered by some philosopher or physicist simply because he is largely ignorant of relevant discussions outside his chosen field of expertise. In these two complementary but independent volumes I have attempted to appraise what I take to be the most important arguments drawn from a variety of fields for and against each theory of time. |
| four-dimensional mathematical model of the universe: Archimedes to Hawking Clifford Pickover, 2008-04-16 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. |
| four-dimensional mathematical model of the universe: The Emergence of the Fourth Dimension Mark Blacklock, 2018-04-05 The Emergence of the Fourth Dimension describes the development and proliferation of the idea of higher dimensional space in the late nineteenth- and early twentieth-centuries. An idea from mathematics that was appropriated by occultist thought, it emerged in the fin de siècle as a staple of genre fiction and influenced a number of important Modernist writers and artists. Providing a context for thinking of space in dimensional terms, the volume describes an active interplay between self-fashioning disciplines and a key moment in the popularisation of science. It offers new research into spiritualism and the Theosophical Society and studies a series of curious hybrid texts. Examining works by Joseph Conrad, Ford Madox Ford, H.G. Wells, Henry James, H. P. Lovecraft, and others, the volume explores how new theories of the possibilities of time and space influenced fiction writers of the period, and how literature shaped, and was in turn shaped by, the reconfiguration of imaginative space occasioned by the n-dimensional turn. A timely study of the interplay between philosophy, literature, culture, and mathematics, it offers a rich resource for readers interested in nineteenth century literature, Modernist studies, science fiction, and gothic scholarship. |
Four - Buy Now, Pay Later
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4 - Wikipedia
4 (four) is a number, numeral and digit. It is the natural number following 3 and preceding 5. It is a square number, the smallest semiprime and composite number, and is considered unlucky in …
Four Seasons at North Caldwell - North Caldwell, NJ - 55Places.com
Four Seasons at North Caldwell is a 55+ community located in tranquil North Caldwell, New Jersey. This active adult community offers beautiful condominiums with spacious layouts and ample …
FOUR Definition & Meaning - Merriam-Webster
The meaning of FOUR is a number that is one more than three. How to use four in a sentence.
Four Definition & Meaning | Britannica Dictionary
“What time is it?” “It's four.” I leave each day at four. Four (of them) are broken.
Four - definition of four by The Free Dictionary
1. a cardinal number, three plus one. 2. a symbol of this number, 4 or IV or IIII. 3. a set of this many persons or things. 4. a. an automobile powered by a four-cylinder engine. b. the engine itself. 5. …
FOUR | definition in the Cambridge English Dictionary
FOUR meaning: 1. the number 4: 2. a team of four people in rowing, or the boat that they use 3. in cricket, four…. Learn more.
FOUR definition in American English | Collins English Dictionary
7 senses: 1. the cardinal number that is the sum of three and one 2. a numeral, 4, IV, etc, representing this number 3..... Click for more definitions.
Four Definition & Meaning - YourDictionary
The cardinal number between three and five; 4; IV. The fourth in a set or sequence. Any group of four people or things. (countable) The digit or figure 4; an occurrence thereof. Totaling one more …
119 Four Seasons Dr - Apartments.com
Fantastic top/3rd floor unit in the highly sought-after adult 55+ community, The Four Seasons at North Caldwell. This stunning East / South facing unit is sun-filled, with a gracious open floor plan …
Four - Buy Now, Pay Later
Buy Now, Pay Later. Allow your shoppers to pay over time while you get paid today, risk free!
4 - Wikipedia
4 (four) is a number, numeral and digit. It is the natural number following 3 and preceding 5. It is a square number, the smallest semiprime and composite number, and is considered unlucky in …
Four Seasons at North Caldwell - North Caldwell, NJ - 55Places.com
Four Seasons at North Caldwell is a 55+ community located in tranquil North Caldwell, New Jersey. This active adult community offers beautiful condominiums with spacious layouts and ample …
FOUR Definition & Meaning - Merriam-Webster
The meaning of FOUR is a number that is one more than three. How to use four in a sentence.
Four Definition & Meaning | Britannica Dictionary
“What time is it?” “It's four.” I leave each day at four. Four (of them) are broken.
Four - definition of four by The Free Dictionary
1. a cardinal number, three plus one. 2. a symbol of this number, 4 or IV or IIII. 3. a set of this many persons or things. 4. a. an automobile powered by a four-cylinder engine. b. the engine itself. 5. …
FOUR | definition in the Cambridge English Dictionary
FOUR meaning: 1. the number 4: 2. a team of four people in rowing, or the boat that they use 3. in cricket, four…. Learn more.
FOUR definition in American English | Collins English Dictionary
7 senses: 1. the cardinal number that is the sum of three and one 2. a numeral, 4, IV, etc, representing this number 3..... Click for more definitions.
Four Definition & Meaning - YourDictionary
The cardinal number between three and five; 4; IV. The fourth in a set or sequence. Any group of four people or things. (countable) The digit or figure 4; an occurrence thereof. Totaling one more …
119 Four Seasons Dr - Apartments.com
Fantastic top/3rd floor unit in the highly sought-after adult 55+ community, The Four Seasons at North Caldwell. This stunning East / South facing unit is sun-filled, with a gracious open floor plan …
