On The Foundations Of Geometry

Author : David Hilbert
Publisher : Read Books Ltd
Page : 98 pages
File Size : 40,8 Mb
Release : 2014-07-07
Category : Mathematics
ISBN : 9781473395947

Get Book

The Foundations of Geometry by David Hilbert Pdf

This early work by David Hilbert was originally published in the early 20th century and we are now republishing it with a brand new introductory biography. David Hilbert was born on the 23rd January 1862, in a Province of Prussia. Hilbert is recognised as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.

Author : Bertrand Russell
Publisher : DigiCat
Page : 211 pages
File Size : 49,5 Mb
Release : 2022-08-15
Category : Fiction
ISBN : EAN:8596547171324

Get Book

An essay on the foundations of geometry by Bertrand Russell Pdf

DigiCat Publishing presents to you this special edition of "An essay on the foundations of geometry" by Bertrand Russell. 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.

Author : G.E. Martin
Publisher : Springer Science & Business Media
Page : 525 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461257257

Get Book

The Foundations of Geometry and the Non-Euclidean Plane by G.E. Martin Pdf

This book is a text for junior, senior, or first-year graduate courses traditionally titled Foundations of Geometry and/or Non Euclidean Geometry. The first 29 chapters are for a semester or year course on the foundations of geometry. The remaining chap ters may then be used for either a regular course or independent study courses. Another possibility, which is also especially suited for in-service teachers of high school geometry, is to survey the the fundamentals of absolute geometry (Chapters 1 -20) very quickly and begin earnest study with the theory of parallels and isometries (Chapters 21 -30). The text is self-contained, except that the elementary calculus is assumed for some parts of the material on advanced hyperbolic geometry (Chapters 31 -34). There are over 650 exercises, 30 of which are 10-part true-or-false questions. A rigorous ruler-and-protractor axiomatic development of the Euclidean and hyperbolic planes, including the classification of the isometries of these planes, is balanced by the discussion about this development. Models, such as Taxicab Geometry, are used exten sively to illustrate theory. Historical aspects and alternatives to the selected axioms are prominent. The classical axiom systems of Euclid and Hilbert are discussed, as are axiom systems for three and four-dimensional absolute geometry and Pieri's system based on rigid motions. The text is divided into three parts. The Introduction (Chapters 1 -4) is to be read as quickly as possible and then used for ref erence if necessary.

Author : Karol Borsuk
Publisher : Courier Dover Publications
Page : 465 pages
File Size : 47,8 Mb
Release : 2018-11-14
Category : Mathematics
ISBN : 9780486828091

Get Book

Foundations of Geometry by Karol Borsuk Pdf

In Part One of this comprehensive and frequently cited treatment, the authors develop Euclidean and Bolyai-Lobachevskian geometry on the basis of an axiom system due, in principle, to the work of David Hilbert. Part Two develops projective geometry in much the same way. An Introduction provides background on topological space, analytic geometry, and other relevant topics, and rigorous proofs appear throughout the text. Topics covered by Part One include axioms of incidence and order, axioms of congruence, the axiom of continuity, models of absolute geometry, and Euclidean geometry, culminating in the treatment of Bolyai-Lobachevskian geometry. Part Two examines axioms of incidents and order and the axiom of continuity, concluding with an exploration of models of projective geometry.

Author : Gerard Venema
Publisher : Unknown
Page : 0 pages
File Size : 45,6 Mb
Release : 2012
Category : Geometry
ISBN : 0136020585

Get Book

Foundations of Geometry by Gerard Venema Pdf

Normal 0 false false false Foundations of Geometry, Second Edition is written to help enrich the education of all mathematics majors and facilitate a smooth transition into more advanced mathematics courses. The text also implements the latest national standards and recommendations regarding geometry for the preparation of high school mathematics teachers--and encourages students to make connections between their college courses and classes they will later teach. This text's coverage begins with Euclid's Elements, lays out a system of axioms for geometry, and then moves on to neutral geometry, Euclidian and hyperbolic geometries from an axiomatic point of view, and then non-Euclidean geometry. Good proof-writing skills are emphasized, along with a historical development of geometry. The Second Edition streamlines and reorganizes material in order to reach coverage of neutral geometry as early as possible, adds more exercises throughout, and facilitates use of the open-source software Geogebra. This text is ideal for an undergraduate course in axiomatic geometry for future high school geometry teachers, or for any student who has not yet encountered upper-level math, such as real analysis or abstract algebra. It assumes calculus and linear algebra as prerequisites.

Author : C. R. Wylie
Publisher : Courier Corporation
Page : 352 pages
File Size : 45,7 Mb
Release : 2009-05-21
Category : Mathematics
ISBN : 9780486472140

Get Book

Foundations of Geometry by C. R. Wylie Pdf

Explains geometric theories and shows many examples.

Author : Mateusz Hohol
Publisher : Routledge
Page : 315 pages
File Size : 49,5 Mb
Release : 2019-09-12
Category : Psychology
ISBN : 9780429509216

Get Book

Foundations of Geometric Cognition by Mateusz Hohol Pdf

The cognitive foundations of geometry have puzzled academics for a long time, and even today are mostly unknown to many scholars, including mathematical cognition researchers. Foundations of Geometric Cognition shows that basic geometric skills are deeply hardwired in the visuospatial cognitive capacities of our brains, namely spatial navigation and object recognition. These capacities, shared with non-human animals and appearing in early stages of the human ontogeny, cannot, however, fully explain a uniquely human form of geometric cognition. In the book, Hohol argues that Euclidean geometry would not be possible without the human capacity to create and use abstract concepts, demonstrating how language and diagrams provide cognitive scaffolding for abstract geometric thinking, within a context of a Euclidean system of thought. Taking an interdisciplinary approach and drawing on research from diverse fields including psychology, cognitive science, and mathematics, this book is a must-read for cognitive psychologists and cognitive scientists of mathematics, alongside anyone interested in mathematical education or the philosophical and historical aspects of geometry.

Author : Tim Maudlin
Publisher : Oxford University Press
Page : 374 pages
File Size : 48,9 Mb
Release : 2014-02
Category : Mathematics
ISBN : 9780198701309

Get Book

New Foundations for Physical Geometry by Tim Maudlin Pdf

Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.

Author : Johannes Ueberberg
Publisher : Springer Science & Business Media
Page : 259 pages
File Size : 45,6 Mb
Release : 2011-08-26
Category : Mathematics
ISBN : 9783642209727

Get Book

Foundations of Incidence Geometry by Johannes Ueberberg Pdf

Incidence geometry is a central part of modern mathematics that has an impressive tradition. The main topics of incidence geometry are projective and affine geometry and, in more recent times, the theory of buildings and polar spaces. Embedded into the modern view of diagram geometry, projective and affine geometry including the fundamental theorems, polar geometry including the Theorem of Buekenhout-Shult and the classification of quadratic sets are presented in this volume. Incidence geometry is developed along the lines of the fascinating work of Jacques Tits and Francis Buekenhout. The book is a clear and comprehensible introduction into a wonderful piece of mathematics. More than 200 figures make even complicated proofs accessible to the reader.

Author : André 1906- Weil
Publisher : Hassell Street Press
Page : 392 pages
File Size : 52,5 Mb
Release : 2021-09-10
Category : Electronic
ISBN : 1015107672

Get Book

Foundations of Algebraic Geometry. --; 29 by André 1906- Weil Pdf

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author : Clarence Raymond Wylie
Publisher : Unknown
Page : 356 pages
File Size : 45,8 Mb
Release : 1964
Category : Geometry
ISBN : UOM:39015049076121

Get Book

Foundations of Geometry by Clarence Raymond Wylie Pdf

Author : Harvey I. Blau
Publisher : Unknown
Page : 0 pages
File Size : 48,5 Mb
Release : 2003
Category : Mathematics
ISBN : 0130479543

Get Book

Foundations of Plane Geometry by Harvey I. Blau Pdf

Ideal for users who may have little previous experience with abstraction and proof, this book provides a rigorous and unified--yet straightforward and accessible --exposition of the foundations of Euclidean, hyperbolic, and spherical geometry. Unique in approach, it combines an extended theme--the study of a generalized absolute plane from axioms through classification into the three fundamental classical planes--with a leisurely development that allows ample time for mathematical growth. It is purposefully structured to facilitate the development of analytic and reasoning skills and to promote an awareness of the depth, power, and subtlety of the axiomatic method in general, and of Euclidean and non-Euclidean plane geometry in particular. Focus on one main topic--The axiomatic development of the absolute plane--which is pursued through a classification into Euclidean, hyperbolic, and spherical planes. Presents specific models such as the sphere, the Klein-Betrami hyperbolic model, and the "gap" plane. Gradually presents axioms for absolute plane geometry.

Author : Michael Hallett,Ulrich Majer
Publisher : Unknown
Page : 700 pages
File Size : 42,5 Mb
Release : 2004-01-01
Category : Electronic
ISBN : 3540207643

Get Book

David Hilbert's Lectures on the Foundations of Geometry 1891-1902 by Michael Hallett,Ulrich Majer Pdf

Author : Garret Sobczyk
Publisher : Springer Science & Business Media
Page : 373 pages
File Size : 41,5 Mb
Release : 2012-10-26
Category : Mathematics
ISBN : 9780817683856

Get Book

New Foundations in Mathematics by Garret Sobczyk Pdf

The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.

Author : Izu Vaisman
Publisher : CRC Press
Page : 287 pages
File Size : 48,9 Mb
Release : 2020-11-25
Category : Mathematics
ISBN : 9781000110494

Get Book

Foundations of Three-Dimensional Euclidean Geometry by Izu Vaisman Pdf

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.