Plane Projective Geometry
Mathematics may be defined as the subject in which we never know what we are talking about,
nor whether what we are saying is true.
—
Bertrand Russell (1872–1970)Chapter Four
Plane Projective Geometry
Mathematics may be
defined as the subject in which we never know what we are talking about,
nor whether what we are saying is true.
—Bertrand Russell (1872–1970)
Section 4.1 -
Introduction
Historical Overview
Section 4.2 -
Axioms and Basic Definitions
(Reference Section 4.6 Definition of Perspectivity and
Projectivity)
Basic Theorems
(Exercises 4.1–4.6)
Independence of Axioms (Exercises
4.9–4.10)
Section 4.3 -
Principle of Duality in Projective
Geometry (Exercises
4.11–4.15)
(Reference Section 4.6 Definition of Perspectivity and
Projectivity)
Section 4.4 - Desargues' Theorem (Exercises 4.16–4.19)
Section 4.5 -
Harmonic Sets (Exercises
4.20–4.24)
Harmonics and
Music (Exercises
4.25–4.27)
Section 4.6 -
Definition of
Perspectivity and Projectivity (Exercises
4.28–4.29)
Fundamental
Theorem (Exercises 4.30–4.35)
Harmonic
Sets and Projectivity (Exercises 4.36–4.37)
Investigation
Activity (Exercise 4.38)
Alternate
Construction of a Projectivity (Exercises
4.39–4.40)
Section 4.7 -
Conics in the Projective Plane (Exercises
4.41–4.45)
Pascal's
Theorem (Exercises 4.46–4.50)
Tangent Lines
to Point Conics (Exercises 4.51–4.54)
Chapter
Four Exercises. Exercises from all the sections.
Solutions.
Solutions to selected exercises.
Self-Assessment Quizzes.
Quizzes for all sections.
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© Copyright 2005, 2006 - Timothy Peil |
