Geometry In Space PDF Download
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Author | : Melvin Hausner |
Publisher | : Courier Dover Publications |
Total Pages | : 417 |
Release | : 2018-10-17 |
Genre | : Mathematics |
ISBN | : 0486835391 |
Download A Vector Space Approach to Geometry Book in PDF, ePub and Kindle
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.
Author | : Ernst Mach |
Publisher | : |
Total Pages | : 164 |
Release | : 1906 |
Genre | : Geometry |
ISBN | : |
Download Space and Geometry in the Light of Physiological, Psychological and Physical Inquiry Book in PDF, ePub and Kindle
Author | : Steven G. Krantz |
Publisher | : Springer Science & Business Media |
Total Pages | : 311 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461215749 |
Download The Geometry of Domains in Space Book in PDF, ePub and Kindle
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.
Author | : John Tabak |
Publisher | : Infobase Publishing |
Total Pages | : 241 |
Release | : 2014-05-14 |
Genre | : Electronic books |
ISBN | : 0816068763 |
Download Geometry Book in PDF, ePub and Kindle
Greek ideas about geometry, straight-edge and compass constructions, and the nature of mathematical proof dominated mathematical thought for about 2,000 years.
Author | : William M. Ivins |
Publisher | : Courier Corporation |
Total Pages | : 130 |
Release | : 2012-10-16 |
Genre | : Art |
ISBN | : 0486143589 |
Download Art and Geometry Book in PDF, ePub and Kindle
This highly stimulating study observes many historical interrelationships between art and mathematics. It explores ancient and Renaissance painting and sculpture, the development of perspective, and advances in projective geometry.
Author | : Richard Lehrer |
Publisher | : Routledge |
Total Pages | : 520 |
Release | : 1998 |
Genre | : Education |
ISBN | : 0805819487 |
Download Designing Learning Environments for Developing Understanding of Geometry and Space Book in PDF, ePub and Kindle
This volume reflects an appreciation of the interactive roles of subject matter, teacher, student, and technologies in designing classrooms that promote understanding of geometry and space. Although these elements of geometry education are mutually constituted, the book is organized to highlight, first, the editors' vision of a general geometry education; second, the development of student thinking in everyday and classroom contexts; and third, the role of technologies. Rather than looking to high school geometry as the locus--and all too often, the apex--of geometric reasoning, the contributors to this volume suggest that reasoning about space can and should be successfully integrated with other forms of mathematics, starting at the elementary level and continuing through high school. Reintegrating spatial reasoning into the mathematical mainstream--indeed, placing it at the core of K-12 mathematics environments that promote learning with understanding--will mean increased attention to problems in modeling, structure, and design and reinvigoration of traditional topics such as measure, dimension, and form. Further, the editors' position is that the teaching of geometry and spatial visualization in school should not be compressed into a characterization of Greek geometry, but should include attention to contributions to the mathematics of space that developed subsequent to those of the Greeks. This volume is essential reading for those involved in mathematics education at all levels, including university faculty, researchers, and graduate students.
Author | : L.Christine Kinsey |
Publisher | : Springer Science & Business Media |
Total Pages | : 524 |
Release | : 2006-05-09 |
Genre | : Mathematics |
ISBN | : 9781930190092 |
Download Symmetry, Shape and Space Book in PDF, ePub and Kindle
This book will appeal to at least three groups of readers: prospective high school teachers, liberal arts students, and parents whose children are studying high school or college math. It is modern in its selection of topics, and in the learning models used by the authors. The book covers some exciting but non-traditional topics from the subject area of geometry. It is also intended for undergraduates and tries to engage their interest in mathematics. Many innovative pedagogical modes are used throughout.
Author | : Siobhan Roberts |
Publisher | : |
Total Pages | : 0 |
Release | : 2007 |
Genre | : Biography & Autobiography |
ISBN | : 9781846680076 |
Download King of Infinite Space Book in PDF, ePub and Kindle
Geometry is far more than just shapes and numbers. It governs much of our lives, from architecture and data-mining technology to aerodynamic car design, life-like characters in animated movies, the molecules of food, even our own body chemistry. This title discusses the groundbreaking work of Donald Coxeter, the greatest geometer of his age.
Author | : Francesca Biagioli |
Publisher | : Springer |
Total Pages | : 258 |
Release | : 2016-08-22 |
Genre | : Philosophy |
ISBN | : 3319317792 |
Download Space, Number, and Geometry from Helmholtz to Cassirer Book in PDF, ePub and Kindle
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.
Author | : Shing-Tung Yau |
Publisher | : Il Saggiatore |
Total Pages | : 398 |
Release | : 2010-09-07 |
Genre | : Mathematics |
ISBN | : 0465020232 |
Download The Shape of Inner Space Book in PDF, ePub and Kindle
The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.