OVER AND
OVER AGAIN

GENGZHE CHANG and
THOMAS W. SEDERBERG

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
Appendix A: Approximation
Appendix B: Limits and Continuity
Appendix C: Convexity
Bibliography
Index

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