In The Search For Beauty Unravelling Non Euclidean Geometry
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In The Search For Beauty: Unravelling Non-euclidean Geometry by Voldemar Smilga Pdf
This is a popular book that chronicles the historical attempts to prove the fifth postulate of Euclid on parallel lines that led eventually to the creation of non-Euclidean geometry. To absorb the mathematical content of the book, the reader should be familiar with the foundations of Euclidean geometry at the high school level. But besides the mathematics, the book is also devoted to stories about the people, brilliant mathematicians starting from Pythagoras and Euclid and terminating with Gauss, Lobachevsky and Klein. For two thousand years, mathematicians tried to prove the fifth postulate (whose formulation seemed to them too complicated to be a real postulate and not a theorem, hence the title In the Search for Beauty). But in the 19th century, they realized that such proof was impossible, and this led to a revolution in mathematics and then in physics. The two final chapters are devoted to Einstein and his general relativity which revealed to us that the geometry of the world we live in is not Euclidean.Also included is an historical essay on Omar Khayyam, who was not only a poet, but also a brilliant astronomer and mathematician.
An engaging exploration of beauty in physics, with a foreword by Nobel Prize–winning physicist Roger Penrose The concept of symmetry has widespread manifestations and many diverse applications—from architecture to mathematics to science. Yet, as twentieth-century physics has revealed, symmetry has a special, central role in nature, one that is occasionally and enigmatically violated. Fearful Symmetry brings the incredible discoveries of the juxtaposition of symmetry and asymmetry in contemporary physics within everyone's grasp. A. Zee, a distinguished physicist and skillful expositor, tells the exciting story of how contemporary theoretical physicists are following Einstein in their search for the beauty and simplicity of Nature. Animated by a sense of reverence and whimsy, Fearful Symmetry describes the majestic sweep and accomplishments of twentieth-century physics—one of the greatest chapters in the intellectual history of humankind.
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.
Like masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever. Now William Dunham gives them the attention they deserve. Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics. A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity. “It is mathematics presented as a series of works of art; a fascinating lingering over individual examples of ingenuity and insight. It is mathematics by lightning flash.” —Isaac Asimov
In the bestselling literary tradition of Lewis Thomas's Lives of a Cell and James Watson's The Double Helix, Poetry of the Universe is a delightful and compelling narrative charting the evolution of mathematical ideas that have helped to illuminate the nature of the observable universe. In a richly anecdotal fashion, the book explores teh leaps of imagination and vision in mathematics that have helped pioneer our understanding of the world around us.
Mathematics and the Physical World by Morris Kline Pdf
Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.
An Enquiry Concerning Human Understanding by David Hume Pdf
Moral philosophy, or the science of human nature, may be treated after two different manners; each of which has its peculiar merit, and may contribute to the entertainment, instruction, and reformation of mankind. The one considers man chiefly as born for action; and as influenced in his measures by taste and sentiment; pursuing one object, and avoiding another, according to the value which these objects seem to possess, and according to the light in which they present themselves. As virtue, of all objects, is allowed to be the most valuable, this species of philosophers paint her in the most amiable colours; borrowing all helps from poetry and eloquence, and treating their subject in an easy and obvious manner, and such as is best fitted to please the imagination, and engage the affections. They select the most striking observations and instances from common life; place opposite characters in a proper contrast; and alluring us into the paths of virtue by the views of glory and happiness, direct our steps in these paths by the soundest precepts and most illustrious examples. They make us feel the difference between vice and virtue; they excite and regulate our sentiments; and so they can but bend our hearts to the love of probity and true honour, they think, that they have fully attained the end of all their labours.
The Cognitive-Theoretic Model of the Universe: A New Kind of Reality Theory by Christopher Michael Langan Pdf
Paperback version of the 2002 paper published in the journal Progress in Information, Complexity, and Design (PCID). ABSTRACT Inasmuch as science is observational or perceptual in nature, the goal of providing a scientific model and mechanism for the evolution of complex systems ultimately requires a supporting theory of reality of which perception itself is the model (or theory-to-universe mapping). Where information is the abstract currency of perception, such a theory must incorporate the theory of information while extending the information concept to incorporate reflexive self-processing in order to achieve an intrinsic (self-contained) description of reality. This extension is associated with a limiting formulation of model theory identifying mental and physical reality, resulting in a reflexively self-generating, self-modeling theory of reality identical to its universe on the syntactic level. By the nature of its derivation, this theory, the Cognitive Theoretic Model of the Universe or CTMU, can be regarded as a supertautological reality-theoretic extension of logic. Uniting the theory of reality with an advanced form of computational language theory, the CTMU describes reality as a Self Configuring Self-Processing Language or SCSPL, a reflexive intrinsic language characterized not only by self-reference and recursive self-definition, but full self-configuration and self-execution (reflexive read-write functionality). SCSPL reality embodies a dual-aspect monism consisting of infocognition, self-transducing information residing in self-recognizing SCSPL elements called syntactic operators. The CTMU identifies itself with the structure of these operators and thus with the distributive syntax of its self-modeling SCSPL universe, including the reflexive grammar by which the universe refines itself from unbound telesis or UBT, a primordial realm of infocognitive potential free of informational constraint. Under the guidance of a limiting (intrinsic) form of anthropic principle called the Telic Principle, SCSPL evolves by telic recursion, jointly configuring syntax and state while maximizing a generalized self-selection parameter and adjusting on the fly to freely-changing internal conditions. SCSPL relates space, time and object by means of conspansive duality and conspansion, an SCSPL-grammatical process featuring an alternation between dual phases of existence associated with design and actualization and related to the familiar wave-particle duality of quantum mechanics. By distributing the design phase of reality over the actualization phase, conspansive spacetime also provides a distributed mechanism for Intelligent Design, adjoining to the restrictive principle of natural selection a basic means of generating information and complexity. Addressing physical evolution on not only the biological but cosmic level, the CTMU addresses the most evident deficiencies and paradoxes associated with conventional discrete and continuum models of reality, including temporal directionality and accelerating cosmic expansion, while preserving virtually all of the major benefits of current scientific and mathematical paradigms.
The Nature of the Physical World by Arthur Stanley Eddington Pdf
DigiCat Publishing presents to you this special edition of "The Nature of the Physical World" by Arthur Stanley Eddington. DigiCat Publishing considers every written word to be a legacy of humankind. Every DigiCat book has been carefully reproduced for republishing in a new modern format. The books are available in print, as well as ebooks. DigiCat hopes you will treat this work with the acknowledgment and passion it deserves as a classic of world literature.
A provocative and thoroughly researched inquiry into what we find beautiful and why, skewering the myth that the pursuit of beauty is a learned behavior. In Survival of the Prettiest, Nancy Etcoff, a faculty member at Harvard Medical School and a practicing psychologist at Massachusetts General Hospital, argues that beauty is neither a cultural construction, an invention of the fashion industry, nor a backlash against feminism—it’s in our biology. Beauty, she explains, is an essential and ineradicable part of human nature that is revered and ferociously pursued in nearly every civilization—and for good reason. Those features to which we are most attracted are often signals of fertility and fecundity. When seen in the context of a Darwinian struggle for survival, our sometimes extreme attempts to attain beauty—both to become beautiful ourselves and to acquire an attractive partner—suddenly become much more understandable. Moreover, if we understand how the desire for beauty is innate, then we can begin to work in our own interests, and not just the interests of our genetic tendencies.
Many scientists believe we are on the verge of a Theory of Everything - a complete unification of all the fundamental forces and particles of nature. In this book, the physicist and author Paul Davies gives an account of the quest for a superforce that will explain how the physical universe is put together. The book describes the bewildering array of subatomic particles that have been discovered in recent years, and shows how their properties form abstract patterns and mathematical symmetries, hinting at deep linkages. It explains how the forces that act between these particles may require the existence of unseen extra dimensions of space, and why the latest bizarre theory suggests that the basic entities out of which all matter is built may not be particles at all, but strings. Aimed at the general reader, this book shows that a unified theory may be within our grasp, and that a single superforce may account not only for the nature of matter, but even for the manner in which the universe came into existence.
The Beauty of Fractals by Heinz-Otto Peitgen,Peter H. Richter Pdf
Now approaching its tenth year, this hugely successful book presents an unusual attempt to publicise the field of Complex Dynamics. The text was originally conceived as a supplemented catalogue to the exhibition "Frontiers of Chaos", seen in Europe and the United States, and describes the context and meaning of these fascinating images. A total of 184 illustrations - including 88 full-colour pictures of Julia sets - are suggestive of a coffee-table book. However, the invited contributions which round off the book lend the text the required formality. Benoit Mandelbrot gives a very personal account, in his idiosyncratic self-centred style, of his discovery of the fractals named after him and Adrien Douady explains the solved and unsolved problems relating to this amusingly complex set.
