
Free Shipping on all Orders Over $35!*
*excludes Marketplace items.
Downloadable: 60 Days
Downloadable: 90 Days
Downloadable: 120 Days
Downloadable: 180 Days
Downloadable: 365 Days
Downloadable: Lifetime Access
This item is being sold by an Individual Seller and will not ship from the Online Bookstore's warehouse. The Seller must confirm the order within two business days. If the Seller refuses to sell or fails to confirm within this time frame, then the order is cancelled.
Please be sure to read the Description offered by the Seller.
Summary
Table of Contents
Preface  p. xiii 
Introduction  p. xxv 
Euclid's Geometry  p. 1 
Very Brief Survey of the Beginnings of Geometry  p. 1 
The Pythagoreans  p. 3 
Plato  p. 5 
Euclid of Alexandria  p. 7 
The Axiomatic Method  p. 9 
Undefined Terms  p. 11 
Euclid's First Four Postulates  p. 15 
The Parallel Postulate  p. 20 
Attempts to Prove the Parallel Postulate  p. 23 
The Danger in Diagrams  p. 25 
The Power of Diagrams  p. 27 
StraightedgeandCompass Constructions, Briefly  p. 29 
Descartes' Analytic Geometry and Broader Idea of Constructions  p. 34 
Briefly on the Number [pi]  p. 38 
Conclusion  p. 40 
Logic and Incidence Geometry  p. 53 
Elementary Logic  p. 53 
Theorems and Proofs  p. 55 
RAA Proofs  p. 58 
Negation  p. 60 
Quantifiers  p. 61 
Implication  p. 64 
Law of Excluded Middle and Proof by Cases  p. 65 
Brief Historical Remarks  p. 66 
Incidence Geometry  p. 69 
Models  p. 72 
Consistency  p. 76 
Isomorphism of Models  p. 79 
Projective and Affine Planes  p. 81 
Brief History of Real Projective Geometry  p. 89 
Conclusion  p. 90 
Hilbert's Axioms  p. 103 
Flaws in Euclid  p. 103 
Axioms of Betweenness  p. 105 
Axioms of Congruence  p. 119 
Axioms of Continuity  p. 129 
Hilbert's Euclidean Axiom of Parallelism  p. 138 
Conclusion  p. 142 
Neutral Geometry  p. 161 
Geometry Without a Parallel Axiom  p. 161 
Alternate Interior Angle Theorem  p. 162 
Exterior Angle Theorem  p. 164 
Measure of Angles and Segments  p. 169 
Equivalence of Euclidean Parallel Postulates  p. 173 
Saccheri and Lambert Quadrilaterals  p. 176 
Angle Sum of a Triangle  p. 183 
Conclusion  p. 190 
History of the Parallel Postulate  p. 209 
Review  p. 209 
Proclus  p. 210 
Equidistance  p. 213 
Wallis  p. 214 
Saccheri  p. 218 
Clairaut's Axiom and Proclus' Theorem  p. 219 
Legendre  p. 221 
Lambert and Taurinus  p. 223 
Farkas Bolyai  p. 225 
The Discovery of NonEuclidean Geometry  p. 239 
Janos Bolyai  p. 239 
Gauss  p. 242 
Lobachevsky  p. 245 
Subsequent Developments  p. 248 
NonEuclidean Hilbert Planes  p. 249 
The Defect  p. 252 
Similar Triangles  p. 253 
Parallels Which Admit a Common Perpendicular  p. 254 
Limiting Parallel Rays, Hyperbolic Planes  p. 257 
Classification of Parallels  p. 262 
Strange New Universe?  p. 264 
Independence of the Parallel Postulate  p. 289 
Consistency of Hyperbolic Geometry  p. 289 
Beltrami's Interpretation  p. 293 
The BeltramiKlein Model  p. 297 
The Poincare Models  p. 302 
Perpendicularity in the BeltramiKlein Model  p. 308 
A Model of the Hyperbolic Plane from Physics  p. 311 
Inversion in Circles, Poincare Congruence  p. 313 
The Projective Nature of the BeltramiKlein Model  p. 333 
Conclusion  p. 346 
Philosophical Implications, Fruitful Applications  p. 371 
What Is the Geometry of Physical Space?  p. 371 
What Is Mathematics About?  p. 374 
The Controversy about the Foundations of Mathematics  p. 376 
The Meaning  p. 380 
The Fruitfulness of Hyperbolic Geometry for Other Branches of Mathematics, Cosmology, and Art  p. 382 
Geometric Transformations  p. 397 
Klein's Erlanger Programme  p. 397 
Groups  p. 399 
Applications to Geometric Problems  p. 403 
Motions and Similarities  p. 408 
Reflections  p. 411 
Rotations  p. 414 
Translations  p. 417 
HalfTurns  p. 420 
Ideal Points in the Hyperbolic Plane  p. 422 
Parallel Displacements  p. 424 
Glides  p. 426 
Classification of Motions  p. 427 
Automorphisms of the Cartesian Model  p. 431 
Motions in the Poincare Model  p. 436 
Congruence Described by Motions  p. 444 
Symmetry  p. 448 
Further Results in Real Hyperbolic Geometry  p. 475 
Area and Defect  p. 476 
The Angle of Parallelism  p. 480 
Cycles  p. 481 
The Curvature of the Hyperbolic Plane  p. 483 
Hyperbolic Trigonometry  p. 487 
Circumference and Area of a Circle  p. 496 
Saccheri and Lambert Quadrilaterals  p. 500 
Coordinates in the Real Hyperbolic Plane  p. 507 
The Circumscribed Cycle of a Triangle  p. 515 
Bolyai's Constructions in the Hyperbolic Plane  p. 520 
Elliptic and Other Riemannian Geometries  p. 541 
Hilbert's Geometry Without Real Numbers  p. 571 
Axioms  p. 597 
Bibliography  p. 603 
Symbols  p. 611 
Name Index  p. 613 
Subject Index  p. 617 
Table of Contents provided by Ingram. All Rights Reserved. 
An electronic version of this book is available through VitalSource.
This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.
By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.
A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.
Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.
Please view the compatibility matrix prior to purchase.