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