Fundamental Concepts of Geometry

Bruce E. Meserve (Autor)

Buch | Softcover

336 Seiten

2003
Dover Publications Inc. (Verlag)
9780486634159 (ISBN)

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Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.

Demonstrates in a clear and lucid manner the relationships between several types of geometry. This highly regarded work is a superior teaching text, especially valuable in teacher preparation, as well as providing an excellent overview of the foundations and historical evolution of geometrical concepts. Preface. Index. Bibliography. Exercises (no solutions). Includes 98 illustrations.

CHAPTER 1. FOUNDATIONS OF GEOMETRY
1-1 Logical systems
1-2 Logical notations
1-3 Inductive and deductive reasoning
1-4 Postulates
1-5 Independent postulates
1-6 Categorical sets of postulates
1-7 A geometry of number triples
1-8 Geometric invariants
CHAPTER 2. SYNTHETIC PROJECTIVE GEOMETRY
2-1 Postulates of incidence and existence
2-2 Properties of a projective plane
2-3 Figures
2-4 Duality
2-5 Perspective figures
2-6 Projective transformations
2-7 Postulate of Projectivity
2-8 Quadrangles
2-9 Complete and simple n-points
2-10 Theorem of Desargues
2-11 Theorem of Pappus
2-12 Conics
2-13 Theorem of Pascal
2-14 Survey
CHAPTER 3. COORDINATE SYSTEMS
3-1 Quadrangular sets
3-2 Properties of quadrangular sets
3-3 Harmonic sets
3-4 Postulates of Separation
3-5 Nets of rationality
3-6 Real projective geometry
3-7 Nonhomogeneous coordinates
3-8 Homogeneous coordinates
3-9 Survey
CHAPTER 4. ANALYTIC PROJECTIVE GEOMETRY
4-1 Representations in space
4-2 Representations on a plane
4-3 Representations on a line
4-4 Matrices
4-5 Cross ratio
4-6 Analytic and synthetic geometries
4-7 Groups
4-8 Classification of projective transformations
4-9 Polarities and conics
4-10 Conics
4-11 Involutions on a line
4-12 Survey
CHAPTER 5. AFFINE GEOMETRY
5-1 Ideal points
5-2 Parallels
5-3 Mid-point
5-4 Classification of conics
5-5 Affine transformations
5-6 Homothetic transformations
5-7 Translations
5-8 Dilations
5-9 Line reflections
5-10 Equiaffine and equiareal transformations
5-11 Survey
CHAPTER 6. EUCLIDEAN PLANE GEOMETRY
6-1 Perpendicluar lines
6-2 Similarity transformations
6-3 Orthogonal line reflections
6-4 Euclidean transformations
6-5 Distances
6-6 Directed angles
6-7 Angles
6-8 Common figures
6-9 Survey
CHAPTER 7. THE EVOLUTION OF GEOMETRY
7-1 Early measurements
7-2 Early Greek influence
7-3 Euclid
7-4 Early euclidean geometry
7-5 The awakening in Europe
7-6 Constructions
7-7 Descriptive geometry
7-8 Seventeenth century
7-9 Eighteenth century
7-10 Euclid's fifth postulate
7-11 Nineteenth and twentieth centuries
7-12 Survey
CHAPTER 8. NONEUCLIDEAN GEOMETRY
8-1 The absolute polarity
8-2 Points and lines
8-3 Hyperbolic geometry
8-4 Elliptic and spherical geometries
8-5 Comparisons
CHAPTER 9. TOPOLOGY
9-1 Topology
9-2 Homeomorphic figures
9-3 Jordan Curve Theorem
9-4 Surfaces
9-5 Euler's Formula
9-6 Tranversable networks
9-7 Four-color problem
9-8 Fixed-point theorems
9-9 Moebius strip
9-10 Survey
BIBLIOGRAPHY
INDEX

Erscheint lt. Verlag	28.3.2003
Sprache	englisch
Maße	136 x 212 mm
Gewicht	345 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-13	9780486634159 / 9780486634159
Zustand	Neuware