Over and Over Again（I***N=9780883856413） pdf kindle caj 下载 azw3 umd 电子版 夸克云

I***ti***, that is transformati*** that are applied to objects

over and over again, are the subject of this book. Three types of

i***tion are c***idered. The first, smoothing, is the process by

which geometrical shapes can be transformed into standard types.

Functional i***tion is a way of describing the phenomenon of

chaos. Finally, i***ti*** 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 soluti*** to problems

involving i***tion, and these are then applied to solve problems

drawn from International Mathematical Olympiads.

1. Transformati*** and their i***tion

2. Arithmetic and geometric means

3. Isoperimetric inequality for ***s

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 manipulati***

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

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书籍介绍

I***ti***, that is transformati*** that are applied to objects over and over again, are the subject of this book. Three types of i***tion are c***idered. The first, smoothing, is the process by which geometrical shapes can be transformed into standard types. Functional i***tion is a way of describing the phenomenon of chaos. Finally, i***ti*** 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 soluti*** to problems involving i***tion, and these are then applied to solve problems drawn from International Mathematical Olympiads.