Download or read book Euclid s Heritage Is Space Three Dimensional written by P. Janich and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: We live in a space, we get about in it. We also quantify it, we think of it as having dimensions. Ever since Euclid's ancient geometry, we have thought of bodies occupying parts of this space (including our own bodies), the space of our practical orientations (our 'moving abouts'), as having three dimensions. Bodies have volume specified by measures of length, breadth and height. But how do we know that the space we live in has just these three dimensions? It is theoreti cally possible that some spaces might exist that are not correctly described by Euclidean geometry. After all, there are the non Euclidian geometries, descriptions of spaces not conforming to the axioms and theorems of Euclid's geometry. As one might expect, there is a history of philosophers' attempts to 'prove' that space is three-dimensional. The present volume surveys these attempts from Aristotle, through Leibniz and Kant, to more recent philosophy. As you will learn, the historical theories are rife with terminology, with language, already tainted by the as sumed, but by no means obvious, clarity of terms like 'dimension', 'line', 'point' and others. Prior to that language there are actions, ways of getting around in the world, building things, being interested in things, in the more specific case of dimensionality, cutting things. It is to these actions that we must eventually appeal if we are to understand how science is grounded.
Download or read book Euclid s Heritage Is Space Three Dimensional written by P. Janich and published by Springer Science & Business Media. This book was released on 1992-11-30 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three spatial characteristics of length, height and depth are used in the same unreflective way by laymen, technicians and scientists alike to describe the forms, positions and measure of bodies and hollow bodies. But how do we know that the space we live in has just these three dimensions? The question has occupied philosophers and scientists since antiquity. The answers proposed have become ever more presumptuous and have increasingly lost sight of everyday intuitions and have sacrificed explanatory power. In Euclid's Heritage Janich shows that all explanations of three-dimensionality hinge on an unreflective geometrical language which seems to accept the lack of an alternative for the three sorts of entities -- points, lines and planes -- that bound the three extended entities -- lines, planes and solids. This is a Euclidean heritage in a dual sense: Euclid himself adopted a geometrical language from the art of figure drawing, and left a tradition of doing geometry as planimetry and of doing stereometry by rotating plane figures. The systematic approach offered here starts out from operational definitions of the spatial forms -- plane, straight edge and perpendicularity -- and proofs that only three planes can intersect pairwise orthogonally. This is the constructive solution in the frame theory of action, providing an unequivocal characterisation of spatial relations in the physical world. The traditional order of geometric concepts turns out to be the most important obstacle to the methodical ordering of everyday scientific concepts.
Download or read book Prolegomena to Analytical Geometry in Anisotropic Euclidean Space of Three Dimensions written by Eric Harold Neville and published by . This book was released on 1922 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Order in Three Dimensional Euclidean and Double Elliptic Spaces written by George Hervey Hallett and published by . This book was released on 1920 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Foundations of Three Dimensional Euclidean Geometry written by Izu Vaisman and published by CRC Press. This book was released on 2020-11-26 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents to the reader a modern axiomatic construction of three-dimensional Euclidean geometry in a rigorous and accessible form. It is helpful for high school teachers who are interested in the modernization of the teaching of geometry.
Download or read book International Tables for Crystallography Mathematical Physical and Chemical Tables written by E. Prince and published by John Wiley & Sons. This book was released on 2004-01-16 with total page 1043 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science. Each of the volumes in the series contains articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials. Emphasis is given to symmetry, diffraction methods and techniques of crystal-structure determination, and the physical and chemical properties of crystals. The data are accompanied by discussions of theory, practical explanations and examples, all of which are useful for teaching. Volume C provides the mathematical, physical and chemical information needed for experimental studies in structural crystallography. This volume covers all aspects of experimental techniques, using all three principal radiation types (X-ray, electron and neutron), from the selection and mounting of crystals and production of radiation, through data collection and analysis, to interpretation of results. Each chapter is supported by a substantial collection of references, and the volume ends with a section on precautions against radiation injury. Eleven chapters have been revised, corrected or updated for the third edition of Volume C. More information on the series can be found at: http://it.iucr.org
Download or read book The Elements of Non Euclidean Geometry written by Duncan M'Laren Young Sommerville and published by . This book was released on 1914 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Progress in Physics vol 1 2011 written by Dmitri Rabounski and published by Infinite Study. This book was released on with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Mathematics
Download or read book Spaces of Constant Curvature written by Joseph Albert Wolf and published by American Mathematical Soc.. This book was released on 2011 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the sixth edition of the classic Spaces of Constant Curvature, first published in 1967, with the previous (fifth) edition published in 1984. It illustrates the high degree of interplay between group theory and geometry. The reader will benefit from the very concise treatments of riemannian and pseudo-riemannian manifolds and their curvatures, of the representation theory of finite groups, and of indications of recent progress in discrete subgroups of Lie groups. Part I is a brief introduction to differentiable manifolds, covering spaces, and riemannian and pseudo-riemannian geometry. It also contains a certain amount of introductory material on symmetry groups and space forms, indicating the direction of the later chapters. Part II is an updated treatment of euclidean space form. Part III is Wolf's classic solution to the Clifford-Klein Spherical Space Form Problem. It starts with an exposition of the representation theory of finite groups. Part IV introduces riemannian symmetric spaces and extends considerations of spherical space forms to space forms of riemannian symmetric spaces. Finally, Part V examines space form problems on pseudo-riemannian symmetric spaces. At the end of Chapter 12 there is a new appendix describing some of the recent work on discrete subgroups of Lie groups with application to space forms of pseudo-riemannian symmetric spaces. Additional references have been added to this sixth edition as well.
Download or read book The Fourth Dimension Simply Explained written by Henry Parker Manning and published by . This book was released on 1910 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Annals of Mathematics written by and published by . This book was released on 1919 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Idealistic Reaction Against Science written by Antonio Aliotta and published by . This book was released on 1914 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Wrinkle in Time written by Madeleine L'Engle and published by Farrar, Straus and Giroux (BYR). This book was released on 2010-04-01 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Encyclop dia Britannica written by Hugh Chisholm and published by . This book was released on 1926 with total page 2342 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Encyclopaedia Britannica Fra to Har written by and published by . This book was released on 1910 with total page 988 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Encyclopaedia Britannica written by Hugh Chisholm and published by . This book was released on 1910 with total page 1976 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Physics Essays written by and published by . This book was released on 1993 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt:
