# Contents

```Preface: Focusing Your Attention

1 Going Down the Drain

1.1	Constructions
1.2	Cobwebs
1.3	Consolidation
1.4	Fibonacci Strikes
1.5	Denouement
Final Break
References

2 A Far Nicer Arithmetic

2.1	General Background: What You Already Know
2.2	Some Special Moduli: Getting Ready for the Fun
2.3	Arithmetic mod p: Some Beautiful Mathematics
2.4	Arithmetic mod Non-primes: The Same But Different
2.5	Primes, Codes, and Security
2.6	Casting Out 9's and 11's: Tricks of the Trade
Final Break

3 Fibonacci and Lucas Numbers

3.1	A Number Trick
3.2	The Explanation Begins
3.3	Divisibility Properties
3.4	The Number Trick Finally Explained
3.6	A Little Geometry!
Final Break
References

4 Paper-Folding and Number Theory

4.1	Introduction: What You Can Do With - and Without -
Euclidean Tools
I Simple Paper-Folding
4.2	Going Beyond Euclid: Folding 2-Period Regular
Polygons
4.3	Folding Numbers
4.4	Some Mathematical Tidbits
II General Paper-Folding
4.5	General Folding Procedures
4.6	The Quasi-Order Theorem
4.7	Appendix: A Little Solid Geometry
Final Break
References

5 Quilts and other Real-World Decorative Geometry

5.1	Quilts
5.2	Variations
5.3	Round and Round
5.4	Up the Wall
Final Break
References

6 Pascal, Euler, Triangles, Windmills,...

6.1	Introduction: A Chance to Experiment
I  Pascal Sets the Scene
6.2	The Binomial Theorem
6.3	The Pascal Triangle and Windmill
6.4	The Pascal Flower and the Generalized
Star of David
II  Euler Takes the Stage
6.5	Eulerian Numbers and Weighted Sums
6.6	Even Deeper Mysteries
References

7 Hair and Beyond

7.1	A Problem with Pigeons, and Related Ideas
7.2	The Biggest Number
7.3	The Big Infinity
7.4	Other Sets of Cardinality ℵ0
7.5	Schroder and Bernstein
7.6	Cardinal Arithmetic
7.7	Even More Infinities?
Final Break
References

8 An Introduction to the Mathematics
of Fractal Geometry

8.1	Introduction to the Introduction: What's
8.2	Intuitive Notion of Self-Similarity
8.3	The Tent Map and the Logistic Map
8.4	Some More Sophisticated Material
Final Break
References

9 Some of Our Own Reflections

9.1	General Principles
9.2	Specific Principles
9.3	Appendix: Principles of Mathematical Pedagogy
References

Index
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