Preface
Acknowledgement
Table of Contents
Part I. Geometric Topics
Chapter 1. Area and Dissection
Section 1. Qualitative and Quantitative Treatments of Area
Section 2. The Bolyai-Gerwin Theorem and Pythagoras? Theorem
Section 3. Dissection Problems
Chapter 2. Projective Geometry
Section 1. Synthetic Approach
Section 2. Metric Approach
Section 3. Analytic Approach
Chapter 3. Conic Sections
Section 1. Loci
Section 2. The Parabola
Section 3. Ellipses and Hyperbolas
Chapter 4. Inversive Geometry
Section 1. Inversion
Section 2. Applications to Euclidean Geometry
Section 3. Mohr-Mascheroni Constructions
Chapter 5. Convexity
Section 1. Figures
Section 2. Convex Figures
Section 3. Figures of Constant Width
Part II. Other Topics
Chapter 6. Balancing Problems
Section 1. Identifying Fake Coins
Section 2. Other Problems
Section 3. Other Balances
Chapter 7. Graph Theory
Section 1. Basic Concepts
Section 2. Trees
Section 3. Directed Graphs
Chapter 8. Beanstalks
Section 1. Red and Blue Beanstalks
Section 2. Infinite Beanstalks
Section 3. Beansprouts
Chapter 9. Inequalities
Section 1. The Rearrangement Inequality
Section 2. The Majorization Inequality
Section 3. Trigonometric Inequalities
Chapter 10. Polynomial Equations
Section 1. Complex Numbers
Section 2. Cubic Equations
Section 3. Quartic Equations.