Foundations Of Geometry

Author : David Hilbert
Publisher : Read Books Ltd
Page : 98 pages
File Size : 51,5 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 : Karol Borsuk
Publisher : Courier Dover Publications
Page : 465 pages
File Size : 52,7 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 : 42,5 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 : G.E. Martin
Publisher : Springer Science & Business Media
Page : 525 pages
File Size : 55,7 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 : Johannes Ueberberg
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 48,5 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 : Tim Maudlin
Publisher : Oxford University Press
Page : 374 pages
File Size : 45,9 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 : Mateusz Hohol
Publisher : Routledge
Page : 315 pages
File Size : 52,8 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 : Bertrand Russell
Publisher : DigiCat
Page : 211 pages
File Size : 42,8 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 : Kazuhiro Fujiwara,Fumiharu Kato
Publisher : Unknown
Page : 863 pages
File Size : 43,8 Mb
Release : 2018
Category : MATHEMATICS
ISBN : 3037196351

Get Book

Foundations of Rigid Geometry I by Kazuhiro Fujiwara,Fumiharu Kato Pdf

Rigid geometry is one of the modern branches of algebraic and arithmetic geometry. It has its historical origin in J. Tate's rigid analytic geometry, which aimed at developing an analytic geometry over non-archimedean valued fields. Nowadays, rigid geometry is a discipline in its own right and has acquired vast and rich structures, based on discoveries of its relationship with birational and formal geometries. In this research monograph, foundational aspects of rigid geometry are discussed, putting emphasis on birational and topological features of rigid spaces. Besides the rigid geometry itself, topics include the general theory of formal schemes and formal algebraic spaces, based on a theory of complete rings which are not necessarily Noetherian. Also included is a discussion on the relationship with Tate's original rigid analytic geometry, V.G. Berkovich's analytic geometry and R. Huber's adic spaces. As a model example of applications, a proof of Nagata's compactification theorem for schemes is given in the appendix. The book is encyclopedic and almost self-contained.

Author : Alexandru Buium
Publisher : American Mathematical Society
Page : 357 pages
File Size : 41,8 Mb
Release : 2023-11-20
Category : Mathematics
ISBN : 9781470475772

Get Book

Foundations of Arithmetic Differential Geometry by Alexandru Buium Pdf

The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is “intrinsically curved”; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.

Author : André 1906- Weil
Publisher : Hassell Street Press
Page : 392 pages
File Size : 55,7 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 : Harvey I. Blau
Publisher : Unknown
Page : 0 pages
File Size : 51,5 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 : Clarence Raymond Wylie
Publisher : Unknown
Page : 356 pages
File Size : 44,9 Mb
Release : 1964
Category : Geometry
ISBN : UOM:39015049076121

Get Book

Foundations of Geometry by Clarence Raymond Wylie Pdf

Author : Philip Brown
Publisher : Mercury Learning and Information
Page : 382 pages
File Size : 44,7 Mb
Release : 2016-03-14
Category : Mathematics
ISBN : 9781944534417

Get Book

Foundations of Mathematics by Philip Brown Pdf

Foundations of Mathematics offers the university student or interested reader a unique reference book by covering the basics of algebra, trigonometry, geometry, and calculus. There are many instances in the book to demonstrate the interplay and interconnectedness of these topics. The book presents definitions and examples throughout for clear, easy learning. Numerous exercises are included at the ends of the chapters, and readers are encouraged to complete all of them as an essential part of working through the book. It offers a unique experience for readers to understand different areas of mathematics in one clear, concise text. Instructors’ resources are available upon adoption. Features: •Covers the basics of algebra, trigonometry, geometry, and calculus •Includes all of the mathematics needed to learn calculus •Demonstrates the interplay and interconnectedness of these topics •Uses numerous examples and exercises to reinforce concepts

Author : Albrecht Beutelspacher,Ute Rosenbaum
Publisher : Cambridge University Press
Page : 272 pages
File Size : 55,8 Mb
Release : 1998-01-29
Category : Mathematics
ISBN : 0521483646

Get Book

Projective Geometry by Albrecht Beutelspacher,Ute Rosenbaum Pdf

Projective geometry is not only a jewel of mathematics, but has also many applications in modern information and communication science. This book presents the foundations of classical projective and affine geometry as well as its important applications in coding theory and cryptography. It also could serve as a first acquaintance with diagram geometry. Written in clear and contemporary language with an entertaining style and around 200 exercises, examples and hints, this book is ideally suited to be used as a textbook for study in the classroom or on its own.