Non-Euclidean Geometry
The Parallel Postulate
History of the Parallel Postulate
History of the Parallel Postulate
History of the Parallel Postulate
History of the Parallel Postulate
Hyperbolic Geometry
Theorem 9.1
Non-intersecting lines
Non-intersecting lines
Theorem 9.2
Theorem 9.2
Theorem 9.2
Theorem 9.2
Omega Triangles
Theorem 9.3
Exterior Angles
Exterior Angles
Theorem 9.4
Theorem 9.4
Theorem 9.5
Theorem 9.6
Saccheri Quadrilaterals
Theorem 9.7
Theorem 9.8
Lambert Quadrilaterals
Theorem 9.9
Angle Measure
Angle Measure
Defect of a Triangle
More Angle Measures
More Angle Measures
More Angle Measures
Gamma Points
Equivalence
Equivalence
Equivalence
Equivalence
Equivalence
Equivalence
Equivalence
Area of a Triangle
Curves
Curves
Curves
Theorems
Theorems
Elliptic Geometry
Theorems
A Model for Elliptic Geometry
A Model for Elliptic Geometry
Consistency
Relative Consistency
Models for Hyperbolic Geometry
The Klein Model
The Klein Model
Models for Hyperbolic Geometry
Poincaré Model
Poincaré Model
Poincaré Model
Distance in the Model
Poincaré Model