OVER AND
OVER AGAIN

Table of Contents

Preface

1. Transformations and their Iteration
2. Arithmetic and Geometric Means
3. Isoperimetric Inequality for Triangles
4. Isoperimetric Quotient
5. Colored Marbles
6. Candy for School Children
7. Sugar Rather Than Candy
8. Checkers on a Circle
9. Decreasing Sets of Positive Integers
10. Matrix Manipulations
11. Nested Triangles
12. Morley's Theorem and Napoleon's Theorem
13. Complex Numbers in Geometry
14. Birth of an IMO Problem
15. Barycentric Coordinates
16. Douglas-Neumann Theorem
17. Lagrange Interpolation
18. The Isoperimetric Problem
19. Formulas for Iterates
20. Convergent Orbits
21. Finding Roots by Iteration
22. Chebyshev Polynomials
23. Sharkovskii's Theorem
24. Variation Diminishing Matrices
25. Approximation by Bernstein Polynomials
26. Properties of Bernstein Polynomials
27. Bémier Curves
28. Cubic Interpolatory Splines
29. Moving Averages
30. Approximation of Surfaces
31. Properties of Triangular Patches
32. Convexity of Patches