Geometry In Space
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The Geometry Of Domains In Space
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Author : Steven G. Krantz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Geometry Of Domains In Space written by Steven G. Krantz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The analysis of Euclidean space is well-developed. The classical Lie groups that act naturally on Euclidean space-the rotations, dilations, and trans lations-have both shaped and guided this development. In particular, the Fourier transform and the theory of translation invariant operators (convolution transforms) have played a central role in this analysis. Much modern work in analysis takes place on a domain in space. In this context the tools, perforce, must be different. No longer can we expect there to be symmetries. Correspondingly, there is no longer any natural way to apply the Fourier transform. Pseudodifferential operators and Fourier integral operators can playa role in solving some of the problems, but other problems require new, more geometric, ideas. At a more basic level, the analysis of a smoothly bounded domain in space requires a great deal of preliminary spadework. Tubular neighbor hoods, the second fundamental form, the notion of "positive reach", and the implicit function theorem are just some of the tools that need to be invoked regularly to set up this analysis. The normal and tangent bundles become part of the language of classical analysis when that analysis is done on a domain. Many of the ideas in partial differential equations-such as Egorov's canonical transformation theorem-become rather natural when viewed in geometric language. Many of the questions that are natural to an analyst-such as extension theorems for various classes of functions-are most naturally formulated using ideas from geometry.
A Vector Space Approach To Geometry
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Author : Melvin Hausner
language : en
Publisher: Courier Dover Publications
Release Date : 2018-10-17
A Vector Space Approach To Geometry written by Melvin Hausner and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-17 with Mathematics categories.
A fascinating exploration of the correlation between geometry and linear algebra, this text portrays the former as a subject better understood by the use and development of the latter rather than as an independent field. The treatment offers elementary explanations of the role of geometry in other branches of math and science — including physics, analysis, and group theory — as well as its value in understanding probability, determinant theory, and function spaces. Outstanding features of this volume include discussions of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. Students and other mathematically inclined readers will find that this inquiry into the interplay between geometry and other areas offers an enriched appreciation of both subjects.
Analytic Hyperbolic Geometry And Albert Einstein S Special Theory Of Relativity Second Edition
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Author : Abraham Albert Ungar
language : en
Publisher: World Scientific Publishing Company
Release Date : 2022
Analytic Hyperbolic Geometry And Albert Einstein S Special Theory Of Relativity Second Edition written by Abraham Albert Ungar and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Mathematics categories.
The World of Discovery Collection is a specially curated selection of children's books that focus on discovering Asia and discovering STEM (Science, Technology, Engineering and Maths). Under the guidance of Dr Ruth Y L Wong, these books aim to promote reading for pleasure, while exciting kids through discovery. With 51 books in this inaugural batch, and with more to come, the books are divided into three levels depending on the child's reading ability: A (Achieving), B (Blooming) and C (Confident). Level B Set 2 features nine titles, exploring themes of science, imagination, nature and global stories. Intended outcomes of Level B include teaching children to be able to: - follow a text when it is being read aloud - turn the page at the right time - sound out at least 70% of the words in the book - read simple sentences - enjoy being read to Each book includes a story-based activity at the end of the books to help parents and educators get children to engage with the story. Includes these 9 titles: Brave Beachley (Sisu Girls series) Brave Beachley tells the tale of Australian Layne Beachley and how she chased her dream to become a world champion surfer. Because tough times are sure to happen. They are part and parcel of life's plan. But don't let those tough times stop you, pick yourself up and say: 'I CAN!' Fearless Frosty (Sisu Girls series) Fearless Frosty tells the story of New Zealander Anna Frost and how she chased her dream to become a professional mountain runner. Whatever it is, go after it. Find the thing that makes you fly! Because one thing is for certain: You'll never know unless you try. Mighty Mira (Sisu Girls series) Mighty Mira tells the tale of Nepali Mira Rai and how she chased her dream to become a professional mountain runner. The moral of my story; Live the moment, live the now. Don't worry if you don't know the path, Have courage, and you'll discover how. Panjang: The Tall Boy Who Became Prime Minister Panjang is the tallest kid around. He hates standing out, but little does he know, he's on his way to greater heights ... This book tells the childhood story of Singapore's second prime minister, Goh Chok Tong, and how he conquered his self-consciousness to become a leader. This tall tale inspires children to embrace the things that make them different. Tun Dr Siti Hasmah Mohd Ali: The Accidental Doctor Meet Siti Hasmah, a little girl, who wanted to be a journalist, in a period when not every girl was sent to school. Find out how she coped when World War II struck. Walk in her footsteps as she graduated from university and went on to save the lives of many Malaysian women and children. See what she finally ended up being. Meme the Monkey: Wins in Life We all like to win and do well. But what does it really mean to win in life? Meme the Monkey wants to do well and tries her very best to. But she soon learns that doing well in life is not just about scoring high marks in her exams - there are other more important things. I Really, Really Don't Like Water! (Wow Wild Asia series) Boleh the otter pup really, really does not like water. Mama starts him on swimming lessons. What should he do? Can he ever get used to the water? Read Boleh's splashy tale of learning new skills and the good surprise that comes with it. I Really, Really Don't Like Heights! (Wow Wild Asia series) Sayang the Leopard cub really, really does not like heights. When Sayang playfully chases after the bird, he ends too high up in a tree. Can Bear, Monkey and Squirrel help Sayang find his footing and courage to climb down the tree? I Really, Really Don't Like Bees! (Wow Wild Asia series) Tahan the bear cub really, really does not like bees. Tahan is nervous when he joins Papa for his first trip to a beehive. Will he succeed in collecting any honey? Can he ever put up with buzzing, swarming bees?
Space And Geometry
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Author : Ernst Mach
language : en
Publisher: Courier Corporation
Release Date : 2004-09-01
Space And Geometry written by Ernst Mach and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-01 with Science categories.
These three essays by an eminent scientist explore the nature, origin, and development of our concepts of space from the points of view of the senses, history, and physics. They examine the subject from every direction, in a manner suitable for both undergraduates and other readers. 25 figures.1906 edition.
Mathematizing Space
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Author : Vincenzo De Risi
language : en
Publisher: Birkhäuser
Release Date : 2015-01-31
Mathematizing Space written by Vincenzo De Risi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-31 with Mathematics categories.
This book collects the papers of the conference held in Berlin, Germany, 27-29 August 2012, on 'Space, Geometry and the Imagination from Antiquity to the Modern Age'. The conference was a joint effort by the Max Planck Institute for the History of Science (Berlin) and the Centro die Ricerca Matematica Ennio De Giorgi (Pisa).
The Shape Of Space
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Author : Jeffrey R. Weeks
language : en
Publisher: CRC Press
Release Date : 2001-12-12
The Shape Of Space written by Jeffrey R. Weeks and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-12-12 with Mathematics categories.
Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.
Geometry
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Author : John Tabak
language : en
Publisher: Infobase Publishing
Release Date : 2014-05-14
Geometry written by John Tabak and has been published by Infobase Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Electronic books categories.
Greek ideas about geometry, straight-edge and compass constructions, and the nature of mathematical proof dominated mathematical thought for about 2,000 years.
A Mathematical Space Odyssey
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Author : Claudi Alsina
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-12-31
A Mathematical Space Odyssey written by Claudi Alsina and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-31 with Mathematics categories.
Solid geometry is the traditional name for what we call today the geometry of three-dimensional Euclidean space. This book presents techniques for proving a variety of geometric results in three dimensions. Special attention is given to prisms, pyramids, platonic solids, cones, cylinders and spheres, as well as many new and classical results. A chapter is devoted 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. The book includes a selection of Challenges for each chapter with solutions, references and a complete index. The text is aimed at secondary school and college and university teachers as an introduction to solid geometry, as a supplement in problem solving sessions, as enrichment material in a course on proofs and mathematical reasoning, or in a mathematics course for liberal arts students.--
Space Number And Geometry From Helmholtz To Cassirer
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Author : Francesca Biagioli
language : en
Publisher: Springer
Release Date : 2016-08-22
Space Number And Geometry From Helmholtz To Cassirer written by Francesca Biagioli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-22 with Philosophy categories.
This book offers a reconstruction of the debate on non-Euclidean geometry in neo-Kantianism between the second half of the nineteenth century and the first decades of the twentieth century. Kant famously characterized space and time as a priori forms of intuitions, which lie at the foundation of mathematical knowledge. The success of his philosophical account of space was due not least to the fact that Euclidean geometry was widely considered to be a model of certainty at his time. However, such later scientific developments as non-Euclidean geometries and Einstein’s general theory of relativity called into question the certainty of Euclidean geometry and posed the problem of reconsidering space as an open question for empirical research. The transformation of the concept of space from a source of knowledge to an object of research can be traced back to a tradition, which includes such mathematicians as Carl Friedrich Gauss, Bernhard Riemann, Richard Dedekind, Felix Klein, and Henri Poincaré, and which finds one of its clearest expressions in Hermann von Helmholtz’s epistemological works. Although Helmholtz formulated compelling objections to Kant, the author reconsiders different strategies for a philosophical account of the same transformation from a neo-Kantian perspective, and especially Hermann Cohen’s account of the aprioricity of mathematics in terms of applicability and Ernst Cassirer’s reformulation of the a priori of space in terms of a system of hypotheses. This book is ideal for students, scholars and researchers who wish to broaden their knowledge of non-Euclidean geometry or neo-Kantianism.
Space Time And Geometry
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Author : Patrick Suppes
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Space Time And Geometry written by Patrick Suppes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The articles in this volume have been stimulated in two different ways. More than two years ago the editor of Synthese, laakko Hintikka, an nounced a special issue devoted to space and time, and articles were solicited. Part of the reason for that announcement was also the second source of papers. Several years ago I gave a seminar on special relativity at Stanford, and the papers by Domotor, Harrison, Hudgin, Latzer and myself partially arose out of discussion in that seminar. All of the papers except those of Griinbaum, Fine, the second paper of Friedman, and the paper of Adams appeared in a special double issue of Synthese (24 (1972), Nos. 1-2). I am pleased to have been able to add the four additional papers mentioned in making the special issue a volume in the Synthese Library. Of these four additional articles, only the one by Fine has pre viously appeared in print (Synthese 22 (1971),448--481); its relevance to the present volume is apparent. In preparing the papers for publication and in carrying out the various editorIal chores of such a task, I am very much indebted to Mrs. Lillian O'Toole for her extensive assistance. INTRODUCTION The philosophy of space and time has been of permanent importance in philosophy, and most of the major historical figures in philosophy, such as Aristotle, Descartes and Kant, have had a good deal to say about the nature of space and time.