Author | Millman, Richard S. author |
---|---|
Title | Geometry [electronic resource] : A Metric Approach with Models / by Richard S. Millman, George D. Parker |
Imprint | New York, NY : Springer US, 1981 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-0130-1 |
Descript | online resource |
1 Preliminary Notions -- 1.1 Axioms and Models -- 1.2 Sets and Equivalence Relations -- 1.3 Functions -- 2 Incidence and Metric Geometry -- 2.1 Definition and Models of Incidence Geometry -- 2.2 Metric Geometry -- 2.3 Special Coordinate Systems -- 3 Betweenness and Elementary Figures -- 3.1 An Alternative Description of the Euclidean Plane -- 3.2 Betweenness -- 3.3 Line Segments and Rays -- 3.4 Angles and Triangles -- 4 Plane Separation -- 4.1 The Plane Separation Axiom -- 4.2 PSA for the Euclidean and Hyperbolic Planes -- 4.3 Pasch Geometries -- 4.4 Interiors and the Crossbar Theorem -- 4.5 Convex Quadrilaterals -- 5 Angle Measure -- 5.1 The Measure of an Angle -- 5.2 The Moulton Plane -- 5.3 Perpendicularity and Angle Congruence -- 5.4 Euclidean and Hyperbolic Angle Measure (optional) -- 6 Neutral Geometry -- 6.1 The Side-Angle-Side Axiom -- 6.2 Basic Triangle Congruence Theorems -- 6.3 The Exterior Angle Theorem and Its Consequences -- 6.4 Right Triangles -- 6.5 Circles and Their Tangent Lines -- 6.6 The Two Circle Theorem (optional) -- 6.7 The Synthetic Approach (optional) -- 7 The Theory of Parallels -- 7.1 The Existence of Parallel Lines -- 7.2 Saccheri Quadrilaterals -- 7.3 The Critical Function -- 8 Hyperbolic Geometry -- 8.1 Asymptotic Rays and Triangles -- 8.2 Angle Sum and the Defect of a Triangle -- 8.3 The Distance Between Parallel Lines -- 9 Euclidean Geometry -- 9.1 Equivalent Forms of EPP -- 9.2 Similarity Theory -- 9.3 Some Classical Theorems of Euclidean Geometry -- 10 Area -- 10.1 The Area Function -- 10.2 The Existence of Euclidean Area -- 10.3 The Existence of Hyperbolic Area -- 10.4 Bolyaiโs Theorem -- 11 The Theory of Isometries -- 11.1 Collineations and Isometries -- 11.2 The Klein and Poincarรฉ Disk Models (optional) -- 11.3 Reflections and the Mirror Axiom -- 11.4 Pencils and Cycles -- 11.5 Double Reflections and Their Invariant Sets -- 11.6 The Classification of Isometries -- 11.7 The Isometry Group -- 11.8 The SAS Axiom in ? -- 11.9 The Isometry Groups of ? and ?