Over and Over Again
Over and Over Again
Thomas W. Sederberg, Brigham Young University, Utah
Iterations, that is transformations that are applied to objects over and over again, are the subject of this book. Three types of iteration are considered. The first, smoothing, is the process by which geometrical shapes can be transformed into standard types. Functional iteration is a way of describing the phenomenon of chaos. Finally, iterations involving curves and surfaces play an important role in computer aided design and graphics. These themes are explored and developed with no more background required than high school mathematics and a little calculus. Several basic strategies are highlighted which unlock solutions to problems involving iteration, and these are then applied to solve problems drawn from International Mathematical Olympiads.
- Uses only elementary mathematics to explain chaos and graphics
- Explains three key ideas that can be used to solve Olympiad questions
- Can be used as resource for maths and computer science courses
Product details
No date availablePaperback
9780883856383
250 pages
216 × 138 mm
0kg
23 b/w illus.
Table of Contents
- 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 traingles
- 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.
