S.M.A.R.T. Circle Minicourses

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.