# OVER AND

OVER AGAIN

### GENGZHE CHANG and

THOMAS W. SEDERBERG

## Table of ContentsPreface - Transformations and their Iteration
- Arithmetic and Geometric Means
- Isoperimetric Inequality for Triangles
- Isoperimetric Quotient
- Colored Marbles
- Candy for School Children
- Sugar Rather Than Candy
- Checkers on a Circle
- Decreasing Sets of Positive Integers
- Matrix Manipulations
- Nested Triangles
- Morley's Theorem and Napoleon's Theorem
- Complex Numbers in Geometry
- Birth of an IMO Problem
- Barycentric Coordinates
- Douglas-Neumann Theorem
- Lagrange Interpolation
- The Isoperimetric Problem
- Formulas for Iterates
- Convergent Orbits
- Finding Roots by Iteration
- Chebyshev Polynomials
- Sharkovskii's Theorem
- Variation Diminishing Matrices
- Approximation by Bernstein Polynomials
- Properties of Bernstein Polynomials
- Bémier Curves
- Cubic Interpolatory Splines
- Moving Averages
- Approximation of Surfaces
- Properties of Triangular Patches
- Convexity of Patches
Appendix B: Limits and Continuity Appendix C: Convexity Bibliography Index |Contact| |Front page| |Contents| |Books| Copyright © 1996-2018 Alexander Bogomolny 71530380 |