The Foundations of Geometry and the Non-Euclidean Plane is a self-contained text for junior, senior, and first-year graduate courses. Historical material is interwoven with a rigorous ruler- and protractor axiomatic development of the Euclidean and hyperbolic planes. Additional topics include the classical axiomatic systems of Euclid and Hilbert, axiom systems for three and four dimensional absolute geometry, and Pieri's system based on rigid motions. Models, such as Taxicab Geometry, are used extensively to illustrate theory.
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Wonderfully clear and complete,
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This review is from: The Foundations of Geometry and the Non-Euclidean Plane (Hardcover)
Though perfectly clear to the mathematician, Non-Euclidean geometry is surronded by an aura of mystery and mistrust among the general public, and even a good many mathematicians would be hard pressed to explain exactly how the negation of the parallel postulate leads to all those strange formulas teeming with hyperbolic functions and other exotica. G.E. Martin explains everything beautifully, with exemplary clarity and just the right amount of detail. The reader also gets a complete construction of Euclidean geometry starting with the Birkhoff-Halsted axiom system, as well as a wealth of historical information into the bargain. Every serious math major or amateur ought to read this book, and many a professional could well benefit from it.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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angle measure function, upper base angles, critical parallelism, odd isometries, piecewise congruent, odd isometry, categorical axiom system, isometry fixes, intersects int, same halfplane, compass game, incidence axiom, absolute geometry, dence plane, preserves betweenness, linear pair, cycle concentric, rusty compass, absolute plane, incidence theorems, parallel postulate, clidean plane, noncollinear points, convex polygonal region, frieze group Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Euclid's Proposition, Proof Suppose, Hypothesis of the Acute Angle, Ruler Postulate, Hypothesis of the Right Angle, Protractor Postulate, Taxicab Geometry, Cayley-Klein Model, Proof Exercise, Pons Asinorum, Saccheri's Proposition, Hypothesis of the Obtuse Angle, Omar Khayyam, Playfair's Parallel Postulate, Euclid's Elements, Construction Theorem, Moulton Incidence Plane, Pasch's Postulate, Proof Follows, Real Cartesian Incidence Plane, Aristotle's Axiom, John Bolyai, King Ptolemy, Nasir Eddin New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
angle measure function, upper base angles, critical parallelism, odd isometries, piecewise congruent, odd isometry, categorical axiom system, isometry fixes, intersects int, same halfplane, compass game, incidence axiom, absolute geometry, dence plane, preserves betweenness, linear pair, cycle concentric, rusty compass, absolute plane, incidence theorems, parallel postulate, clidean plane, noncollinear points, convex polygonal region, frieze group Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Euclid's Proposition, Proof Suppose, Hypothesis of the Acute Angle, Ruler Postulate, Hypothesis of the Right Angle, Protractor Postulate, Taxicab Geometry, Cayley-Klein Model, Proof Exercise, Pons Asinorum, Saccheri's Proposition, Hypothesis of the Obtuse Angle, Omar Khayyam, Playfair's Parallel Postulate, Euclid's Elements, Construction Theorem, Moulton Incidence Plane, Pasch's Postulate, Proof Follows, Real Cartesian Incidence Plane, Aristotle's Axiom, John Bolyai, King Ptolemy, Nasir Eddin New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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62
books
cite this book:
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- Foundations of Geometry by David Hilbert on page 139, page 143, and page 180
- Geometric Exercises in Paper Folding by T. Sundara Row on page 399, and page 493
- The World of Mathematics by James R. Newman on page 46, and page 316
- Men of Mathematics (Touchstone Books) by E.T. Bell on page 63, and page 315
- Famous Problems of Mathematics by Henrich Tietze on page 316
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- Geometry: Euclid and Beyond by Robin Hartshorne in Back Matter (1), and Back Matter (2)
- Geometry: A Metric Approach with Models (Undergraduate Texts in Mathematics) by Richard S. Millman in Back Matter (1), and Back Matter (2)
- Topology of Surfaces (Undergraduate Texts in Mathematics) by L.Christine Kinsey in Back Matter
- Mathematical Reflections by Peter Hilton in Back Matter
- Calculus I (Undergraduate Texts in Mathematics) by Jerrold Marsden in Back Matter
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