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
	Answers for Final Break

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
	Answers for 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
3.5	More About Divisibility
3.6	A Little Geometry!  
	Final Break
	References
	Answers for Final Break

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
	Answers for Final Break

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
	Answers for Final Break

8 An Introduction to the Mathematics 
	of Fractal Geometry

8.1	Introduction to the Introduction: What's 
	Different About Our Approach
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
	Answers for Final Break

9 Some of Our Own Reflections

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

Index

|Up|

|Contact| |Front page| |Contents| |Store| |Books|

Copyright © 1996-2015 Alexander Bogomolny