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61. Foundations of Euclidean and non-Euclidean
 
$109.77
62. The Philosophical Mathematics
$20.99
63. Non-Euclidean Geometry in the
 
64. Rene's Place--exploring Euclidean
 
65. Introduction to Non-Euclidean
$60.46
66. Euclid and His Twentieth Century
 
67. Taxicab Geometry: Adventure in
$52.99
68. Bibliography of Non-Euclidean
$18.10
69. Non-Euclidean Geometry: A Critical
 
70. Non-Euclidean Geometry. Fifth
$14.55
71. Non-Euclidean geometry
72. Shadows of the Circle: Conic Sections,
 
73. Euclidean Geometry
 
$10.00
74. Deductive Systems: Finite and
 
75. A Simple Non-Euclidean Geometry
$134.00
76. Computing in Euclidean Geometry
 
77. Euclidean Geometry and Convexity
$157.98
78. From Affine to Euclidean Geometry:
 
79. Foundations of Euclidean and Non-Euclidean
$27.11
80. A System of the Mathematics: Containing

61. Foundations of Euclidean and non-Euclidean geometry
by Ellery B Golos
 Hardcover: 225 Pages (1968)

Isbn: 0030684951
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62. The Philosophical Mathematics of Isaac Barrow, (1630-1677): Conserving the Ancient Greek Geometry of the Euclidean School
by Gregory Gillette
 Hardcover: 222 Pages (2009-05-30)
list price: US$109.95 -- used & new: US$109.77
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Asin: 0773447725
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Isaac Barrow is largely responsible for that preservation and promulgation of the Euclidean tradition which invigorated the physical science and mathematics of Newton and others, and allowed for an ongoing engagement with classical Greek mathematics. Barrow's philosophy of mathematics remains relevant to many key issues still at the forefront of modern philosophies of mathematics. The tradition of mathematics as a liberal discipline, which is the main topic of this book, reaches back to the educational ideals of Plato and Aristotle, and was brought to an early state of near perfection in the Euclidean school of Greek geometry. Within this framework mathematics is practiced as the means of training and cultivating our formal powers: the intellect and imagination function together to achieve a high degree of familiarity with the geometrical structures, patterns and relations that we find embedded in the world around us. The ultimate goal is liberation of the spirit from exclusive preoccupation with mundane concerns.However, we remain at the same time anchored to a realistic philosophical conception of the world, in which our mathematical notions arise by abstraction from real, objective properties of things outside ourselves. This practice of mathematics as a liberal discipline is exemplified nowhere more completely than in the work of Isaac Barrow. The interplay between these modern philosophies and liberal educational ideals forms a recurrent theme of this book. Separate chapters are devoted to Barrow's development as a translator of Greek mathematics and as a mathematician in his own right; to his contributions to the birth of the infinitesimal calculus; to his conception of geometry as the most fundamental and realistic form of mathematics; to his treatment of physical space and time; and to the philosophical and theological implications of the constructive ideal which lies at the heart of classical geometry. ... Read more


63. Non-Euclidean Geometry in the Theory of Automorphic Functions (History of Mathematics, V. 17)
by Jacques Hadamard (edited by Jeremy J. Gray and Abe Shenitzer)
Paperback: 95 Pages (1999-11-01)
list price: US$21.00 -- used & new: US$20.99
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Asin: 0821820303
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############################################################################################################################################################################################################################################################### ... Read more


64. Rene's Place--exploring Euclidean geometry in Descartes' plane
by L. Roland Genise
 Unknown Binding: 99 Pages (1993)

Isbn: 0201815982
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65. Introduction to Non-Euclidean Geometry
by David Gans
 Hardcover: 274 Pages (1973-06)
list price: US$65.00
Isbn: 0122748506
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66. Euclid and His Twentieth Century Rivals: Diagrams in the Logic of Euclidean Geometry (CSLI-Studies in the Theory and Applications of Diagrams)
by Nathaniel Miller
Hardcover: 119 Pages (2008-07-08)
list price: US$65.00 -- used & new: US$60.46
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Asin: 1575865076
Average Customer Review: 4.0 out of 5 stars
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Twentieth-century developments in logic and mathematics have led many people to view Euclid’s proofs as inherently informal, especially due to the use of diagrams in proofs. In Euclid and His Twentieth-Century Rivals, Nathaniel Miller discusses the history of diagrams in Euclidean Geometry, develops a formal system for working with them, and concludes that they can indeed be used rigorously. Miller also introduces a diagrammatic computer proof system, based on this formal system. This volume will be of interest to mathematicians, computer scientists, and anyone interested in the use of diagrams in geometry.

 

 

 

 

 

 

 

 

 

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Customer Reviews (1)

4-0 out of 5 stars neat computer program for proofs
Most of us first encountered Euclidean geometry in primary school. At those ages, it is a branch of maths that can be taught reasonably rigourously. And from which, there are all these memories of how diagrams are used in proofs. What Miller does here is refresh and expand on this diagrammatic approach. Providing a good review of the fundamentals of geometry, if nothing else.

But the present intrudes, in the form of an elegant computer program with a simple text and graphics output. This program can, with some assistance, find, that is, prove some conjectures. It's really awesome when it gives results! ... Read more


67. Taxicab Geometry: Adventure in Non-Euclidean Geometry (Addison-Wesley innovative series)
by Eugene F. Krause
 Paperback: 96 Pages (1975-11)

Isbn: 0201039346
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Product Description
Develops a simple non-Euclidean geometry and explores some of its practical applications through graphs, research problems, and exercises. Includes selected answers. ... Read more


68. Bibliography of Non-Euclidean Geometry, Including the Theory of Parallels, the Foundations of Geometry, and Space of N Dimensions
by Duncan M'laren Young Sommerville
Paperback: 464 Pages (2010-01-13)
list price: US$52.99 -- used & new: US$52.99
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Asin: 1153301881
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Editorial Review

Product Description
Publisher: London Pub. by Harrison for the University of St. AndrewsPublication date: 1911Subjects: Geometry, Non-EuclideanNotes: This is an OCR reprint. There may be numerous typos or missing text. There are no illustrations or indexes.When you buy the General Books edition of this book you get free trial access to Million-Books.com where you can select from more than a million books for free. You can also preview the book there. ... Read more


69. Non-Euclidean Geometry: A Critical And Historical Study Of Its Development (1912)
by Roberto Bonola
Paperback: 284 Pages (2007-10-17)
list price: US$27.95 -- used & new: US$18.10
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Asin: 054863243X
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Editorial Review

Product Description
This scarce antiquarian book is a selection from Kessinger Publishings Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the worlds literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more


70. Non-Euclidean Geometry. Fifth edition.
by H S M Coxeter
 Hardcover: Pages (1965)

Asin: B003HJ712G
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71. Non-Euclidean geometry
by Henry Parker Manning
Paperback: 114 Pages (2010-08-23)
list price: US$19.75 -- used & new: US$14.55
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Asin: 1177650886
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Product Description
Originally published in 1901.This volume from the Cornell University Library's print collections was scanned on an APT BookScan and converted to JPG 2000 format by Kirtas Technologies.All titles scanned cover to cover and pages may include marks notations and other marginalia present in the original volume. ... Read more


72. Shadows of the Circle: Conic Sections, Optimal Figures and Non-Euclidean Geometry
by Vagn Lundsgaard Hansen
Hardcover: 111 Pages (1998-03)
list price: US$16.00
Isbn: 981023418X
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Product Description
This work offers insights on various facets of geometry through development of four geometric themes: ellipse, the shape or shadow cast by a cirlce; all three types of conic sections - the ellipse, the parabola and the hyperbola; certain properties of geometric figures related to the problem of finding the largest areas that can be enclosed by a curve of given length - the isoperimetric problem; and a development of the non-Euclidean geometry in the Poincare disc model of the hyperbolic plane. ... Read more


73. Euclidean Geometry
by J.A. Gillet
 Hardcover: Pages (1896)

Asin: B003G7RWOQ
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A geometry math book. ... Read more


74. Deductive Systems: Finite and Non-Euclidean Geometries
by Garth E. Runion
 Paperback: 90 Pages (1978-06)
list price: US$10.95 -- used & new: US$10.00
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Asin: 0873531299
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75. A Simple Non-Euclidean Geometry and Its Physical Basis: An Elementary Account of Galilean Geometry and the Galilean Principle of Relativity (Heidelberg Science Library)
by I.M. Yaglom
 Paperback: 307 Pages (1979-02-28)
list price: US$51.95
Isbn: 0387903321
Average Customer Review: 3.5 out of 5 stars
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Customer Reviews (2)

4-0 out of 5 stars A Simple Non-Euclidean Geometry and Its Physical Basis
This book does an excellent job of describing Galilean Geometry.I know of no other books on the topic, and this one was hard to find.It was used as a reference in an advanced mathematics course on geometries in 2010.There are a handful of points that were confusing in the text, but for the most part it is a fine book for self-study.There is an introduction, two main chapters on Galilean geometry, and a shorter final chapter on Minkowskian geometry.Each chapter ends with about twenty problems and several open ended challenge problems.About 25% of those problems have answers or hints in the back of the book, but they tend to be fairly cryptic.Pages 214-288 are three appendices describing a set of nine geometries to which the ones presented belong.

The level of the text calls for a solid mastery of trigonometry, but requires no calculus, although a few limits appear in the appendices.Also required is a fair bit of mathematical insight and creativity.The subject is not for the faint of heart;of the several geometries studied in the course, this was by far the most involved.The book has particular appeal to physicists, as Galilean geometry is rarely even mentioned anywhere else, but is useful as a way of comparing classical and Einsteinian relativity.

3-0 out of 5 stars Thorough Galilean geometry
Galilean geometry is the study of the x-t plane under the motions that correspond to changes in time origin and change of uniform motion coordinate system. Although we introduce this geometry on physical grounds, we quickly move on to study this geometry in its own right without any physical motivation. Distance in Galilean geometry should mean distance in space and not in time so the distance between two points is the distance between their projections on the x-axis. Therefore circles in Galilean geometry are pairs of lines t=constant. The angle between two lines can be defined in terms of the section they cut out of a circle centred at their intersection, so in this way we have angles in Galilean geometry. But circles can also be defined in terms of angles: a moving point on a circle makes a constant angle with any two fixed points of the circle (half the central angle). Applying this definition in Galilean geometry gives a new type of curve which we call cycles. Circles and cycles together are in many ways the natural analog of Euclidean circles. We see this in particular when we study circle inversion. Euclidean circle inversion can be understood in terms of stereographic projection: put the plane tangent to the south pole and the eye at the north pole and project up on the sphere, then interchange the plane and the eye and project back. In Galilean geometry the sphere must be replaced by a cylinder (since, e.g., the center of the circle t=-c, t=+c is the line t=0 and thus maps to a line at infinity). In the chapter called "Conclusion" we look at how our ideas carry over to the geometry of space-time in special relativity, again without much concern for physics. As before, we use physics only to derive the motions of our geometry, in this case the Lorentz transformations, and then quickly go on to consider things of purely geometric interest. For instance, we see that the difference in signs between space and time components of a Lorentz transformation implies that a circle will be a hyperbola x^2-t^2=0 and the analog of stereographic projection requires a hyperboloid. ... Read more


76. Computing in Euclidean Geometry (Lecture Notes Series on Computing)
by Ding-Zhu Du
Hardcover: 492 Pages (1995-05)
list price: US$134.00 -- used & new: US$134.00
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Asin: 9810218761
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Editorial Review

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This book is a collection of surveys and exploratory articlesabout recent developments in the field of computational Euclideangeometry. Topics covered include the history of Euclidean geometry,Voronoi diagrams, randomized geometric algorithms, computationalalgebra, triangulations, machine proofs, topological designs,finite-element mesh, computer-aided geometric designs and Steinertrees. This second edition contains three new surveys coveringgeometric constraint solving, computational geometry and the exactcomputation paradigm. ... Read more


77. Euclidean Geometry and Convexity
by Russell Benson
 Hardcover: 265 Pages (1966)

Isbn: 0070047707
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78. From Affine to Euclidean Geometry: An Axiomatic Approach
by W. Szmielew
Hardcover: 212 Pages (1983-08-31)
list price: US$169.00 -- used & new: US$157.98
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Asin: 9027712433
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79. Foundations of Euclidean and Non-Euclidean Geometry (Pure and Applied Mathematics)
by Richard L. Faber
 Hardcover: 352 Pages (1983-01-28)
list price: US$70.00
Isbn: 0824717481
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80. A System of the Mathematics: Containing the Euclidean Geometry, Plane & Spherical Trigonometry ... Astronomy, the Use of the Globes & Navigation ... Also ... Useful Table of the Latitudes & Longitud
by James Hodgson
Paperback: 712 Pages (2010-04-20)
list price: US$49.75 -- used & new: US$27.11
(price subject to change: see help)
Asin: 1148937765
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Editorial Review

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more


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