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

Bibliographic Details
Main Author: Liu, Andrew Chiang-Fung (Author)
Corporate Author: SpringerLink (Online service)
Summary:XIV, 244 p. 173 illus.
text
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
Edition:1st ed. 2018.
Series:Springer Texts in Education,
Subjects:
Online Access:https://doi.org/10.1007/978-3-319-71743-2
Format: Electronic Book
Table of Contents:
  • 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.