a mathematical space odyssey solid geometry in the 21st century

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A Mathematical Space Odyssey

Author : Claudi Alsina
ISBN : 9780883853580
Genre : Mathematics
File Size : 70. 2 MB
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Solid geometry is the traditional name for what we call today the geometry of three-dimensional Euclidean space. Courses in solid geometry have largely disappeared from American high schools and colleges. The authors are convinced that a mathematical exploration of three-dimensional geometry merits some attention in today’s curriculum. A Mathematical Space Odyssey: Solid Geometry in the 21st Century is devoted to presenting techniques for proving a variety of mathematical results in three-dimensional space, techniques that may improve one’s ability to think visually. Special attention is given to the classical icons of solid geometry (prisms, pyramids, platonic solids, cones, cylinders, and spheres) and many new and classical results: Cavalieri’s principle, Commandino’s theorem, de Gua’s theorem, Prince Rupert’s cube, the Menger sponge, the Schwarz lantern, Euler’s rotation theorem, the Loomis-Whitney inequality, Pythagorean theorems in three dimensions, etc. The authors devote a chapter to each of the following basic techniques for exploring space and proving theorems: enumeration, representation, dissection, plane sections, intersection, iteration, motion, projection, and folding and unfolding. In addition to many figures illustrating theorems and their proofs, a selection of photographs of three-dimensional works of art and architecture are included. Each chapter includes a selection of Challenges for the reader to explore further properties and applications. It concludes with solutions to all the Challenges in the book, references, and a complete index. Readers should be familiar with high school algebra, plane and analytic geometry, and trigonometry. While brief appearances of calculus do occur, no knowledge of calculus is necessary to enjoy this book.

Icons Of Mathematics

Author : Claudi Alsina
ISBN : 9780883853528
Genre : Mathematics
File Size : 44. 55 MB
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The authors present twenty icons of mathematics--that is, geometrical shapes such as the right triangle, the Venn diagram, and the yang and yin symbol--and explore mathematical results associated with them. As with their previous books (Charming Proofs, When Less is More, Math Made Visual) proofs are visual whenever possible.The results require no more than high-school mathematics to appreciate and many of them will be new even to experienced readers. Besides theorems and proofs, the book contains many illustrations and it gives connections of the icons to the world outside of mathematics. There are also problems at the end of each chapter, with solutions provided in an appendix.The book could be used by students in courses in problem solving, mathematical reasoning, or mathematics for the liberal arts. It could also be read with pleasure by professional mathematicians, as it was by the members of the Dolciani editorial board, who unanimously recommend its publication.

Thinking Geometrically

Author : Thomas Q. Sibley
ISBN : 9781939512086
Genre : Mathematics
File Size : 72. 69 MB
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Thinking Geometrically: A Survey of Geometries is a well written and comprehensive survey of college geometry that would serve a wide variety of courses for both mathematics majors and mathematics education majors. Great care and attention is spent on developing visual insights and geometric intuition while stressing the logical structure, historical development, and deep interconnectedness of the ideas. Students with less mathematical preparation than upper-division mathematics majors can successfully study the topics needed for the preparation of high school teachers. There is a multitude of exercises and projects in those chapters developing all aspects of geometric thinking for these students as well as for more advanced students. These chapters include Euclidean Geometry, Axiomatic Systems and Models, Analytic Geometry, Transformational Geometry, and Symmetry. Topics in the other chapters, including Non-Euclidean Geometry, Projective Geometry, Finite Geometry, Differential Geometry, and Discrete Geometry, provide a broader view of geometry. The different chapters are as independent as possible, while the text still manages to highlight the many connections between topics. The text is self-contained, including appendices with the material in Euclid’s first book and a high school axiomatic system as well as Hilbert’s axioms. Appendices give brief summaries of the parts of linear algebra and multivariable calculus needed for certain chapters. While some chapters use the language of groups, no prior experience with abstract algebra is presumed. The text will support an approach emphasizing dynamical geometry software without being tied to any particular software.

Geometry Illuminated

Author : Matthew Harvey
ISBN : 9781939512116
Genre : Mathematics
File Size : 66. 54 MB
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Geometry Illuminated is an introduction to geometry in the plane, both Euclidean and hyperbolic. It is designed to be used in an undergraduate course on geometry, and as such, its target audience is undergraduate math majors. However, much of it should be readable by anyone who is comfortable with the language of mathematical proof. Throughout, the goal is to develop the material patiently. One of the more appealing aspects of geometry is that it is a very "visual" subject. This book hopes to takes full advantage of that, with an extensive use of illustrations as guides. Geometry Illuminated is divided into four principal parts. Part 1 develops neutral geometry in the style of Hilbert, including a discussion of the construction of measure in that system, ultimately building up to the Saccheri-Legendre Theorem. Part 2 provides a glimpse of classical Euclidean geometry, with an emphasis on concurrence results, such as the nine-point circle. Part 3 studies transformations of the Euclidean plane, beginning with isometries and ending with inversion, with applications and a discussion of area in between. Part 4 is dedicated to the development of the Poincaré disk model, and the study of geometry within that model. While this material is traditional, Geometry Illuminated does bring together topics that are generally not found in a book at this level. Most notably, it explicitly computes parametric equations for the pseudosphere and its geodesics. It focuses less on the nature of axiomatic systems for geometry, but emphasizes rather the logical development of geometry within such a system. It also includes sections dealing with trilinear and barycentric coordinates, theorems that can be proved using inversion, and Euclidean and hyperbolic tilings.

Historical Encyclopedia Of Nursing

Author : Mary Ellen Snodgrass
ISBN : 0756770831
Genre : Medical
File Size : 27. 48 MB
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Nurses have been the foot soldiers of med., treating battlefield casualties, caring for the poor, comforting the dying, and fighting maladies ranging from TB and polio to AIDS. Here is the story of nursing from Roman times to the present, focusing on significant events, eras of conflict and social change, treatment innovations, landmark institutions, champions of women's health, and the evolution of mil. nursing. Covers important individuals, key nursing concepts, famous breakthroughs, historical eras, med., abortion pros and cons, ethnic cures, hospices, midwifery, native healers, hospital ships, Cadet Nurse Corps, pub's., and more. Includes a timeline of landmarks in nursing history and a detailed biblio. Numerous bio's. of healthcare pioneers and activists. Illus.

Hyperspace

Author : Michio Kaku
ISBN : 9780191037108
Genre : Science
File Size : 70. 72 MB
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Already thoroughly familiar to the seasoned science fiction fan, Hyperspace is that realm which enables a spaceship captain to take his ship on a physics-defying shortcut (or "wormhole") to the outer shores of the Galaxy in less time than it takes a 747 to fly from New York to Tokyo. But in the past few years, physicists on the cutting edge of science have found that a 10-dimensional Hyperspace may actually exist, albeit at a scale almost too small to comprehend, smaller even than a quark; and that in spite of its tiny size, it may be the basis on which all the forces of nature will be united. This is the first book for a general audience on one of the latest, most exciting developments in modern science. In the past several years, theoretical physicists—the author among them—have discovered that the universe exists not merely in the four spacetime dimensions (3 of space + one of time) with which Einstein made us familiar, but rather as a ten-dimensional Hyperspace. Once the domain of the science fiction writer or the occultist, Hyperspace has recently been shown to be the only kind of space in which the laws of modern physics can be satisfactorily explained. Amazingly enough, many of the phenomena whose explanations have stymied 20th century physicists and cosmologists can now be perfectly clarified by using the ten dimensions of Hyperspace. Most importantly, Einstein's unfulfilled dream, the work on which he spent the last several decades of his life in vain—the unification of all the forces of nature—now sits waiting on the ten-dimensional doorstep of modern theoretical physicists. Michio Kaku—theoretical high-energy physicist, author, radio talkshow host, and nuclear disarmament activist—is one of the pioneers in the field of String Theory, which states that the basic constituents of our universe are not quarks or protons or electrons, but much smaller entities called "strings" or "superstrings", which vibrate—like violin strings—in 10 dimensional Hyperspace, and whose vibrations in different resonances are manifested in the elementary particles. In his book, Kaku takes the reader on a ride through Hyperspace to the edge of physics. On the way he gives crystal clear explanations of such formidable mathematical concepts as non-Euclidean Geometry, Kaluza-Klein Theory, and Supergravity, the everyday tools of the string theorist. Utilizing fascinating and often hilarious anecdotes from history, from art, and from science fiction, Kaku shows us that writers and artists—in addition to scientists—have been fascinated by multidimensional space for over a century. In fact, many of the weird effects created by such famous artists as Dali and Picasso can be explained and more appreciated with an eye on the fourth spatial dimension. Finally, Kaku shows us why the ability to master Hyperspace may be our only salvation from destruction at the end of space-time. This lively yet authoritative book is spiced with many whimsical illustrations in a style reminiscent of the late science writer George Gamow.

Mathematics And The Unexpected

Author : Ivar Ekeland
ISBN : 0226199908
Genre : Mathematics
File Size : 56. 84 MB
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"Not the least unexpected thing about Mathematics and the Unexpected is that a real mathematician should write not just a literate work, but a literary one."—Ian Stewart, New Scientist "In this brief, elegant treatise, assessable to anyone who likes to think, Ivar Ekelund explains some philosophical implications of recent mathematics. He examines randomness, the geometry involved in making predictions, and why general trends are easy to project (it will snow in January) but particulars are practically impossible (it will snow from 2 p.m. to 5 p.m. on the 21st)."—Village Voice

When Less Is More

Author : Claudi Alsina
ISBN : 0883853426
Genre : Mathematics
File Size : 61. 31 MB
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Introduces the richness and variety of inequalities in mathematics using illustration and visualisation.

Great Moments In Mathematics Before 1650

Author : Howard Whitley Eves
ISBN : 0883853108
Genre : Mathematics
File Size : 36. 42 MB
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Presents a series of lectures on the history of mathematics covering such topics as the Pythagorean Theorem, Archimedes, and Fibonacci.

Video Game Spaces

Author : Michael Nitsche
ISBN : 9780262293013
Genre : Games
File Size : 53. 9 MB
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The move to 3D graphics represents a dramatic artistic and technical development in the history of video games that suggests an overall transformation of games as media. The experience of space has become a key element of how we understand games and how we play them. In Video Game Spaces, Michael Nitsche investigates what this shift means for video game design and analysis. Navigable 3D spaces allow us to crawl, jump, fly, or even teleport through fictional worlds that come to life in our imagination. We encounter these spaces through a combination of perception and interaction. Drawing on concepts from literary studies, architecture, and cinema, Nitsche argues that game spaces can evoke narratives because the player is interpreting them in order to engage with them. Consequently, Nitsche approaches game spaces not as pure visual spectacles but as meaningful virtual locations. His argument investigates what structures are at work in these locations, proceeds to an in-depth analysis of the audiovisual presentation of gameworlds, and ultimately explores how we use and comprehend their functionality. Nitsche introduces five analytical layers -- rule-based space, mediated space, fictional space, play space, and social space -- and uses them in the analyses of games that range from early classics to recent titles. He revisits current topics in game research, including narrative, rules, and play, from this new perspective. Video Game Spaces provides a range of necessary arguments and tools for media scholars, designers, and game researchers with an interest in 3D game worlds and the new challenges they pose.

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