Author | Hilton, Peter. author |
---|---|
Title | Mathematical Reflections [electronic resource] : In a Room with Many Mirrors / by Peter Hilton, Derek Holton, Jean Pedersen |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1997 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1932-3 |
Descript | XVI, 352 p. online resource |
1 Going Down the Drain -- 1.1 Constructions -- 1.2 Cobwebs -- 1.3 Consolidation -- 1.4 Fibonacci Strikes -- 1.5 Dรฉnouement -- 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 9โs and 11โs: Tricks of the Trade -- 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! -- 4 Paper-Folding and Number Theory -- 4.1 Introduction: What You Can Do Withโand WithoutโEuclidean Tools -- 4.2 Going Beyond Euclid: Folding 2-Period Regular Polygons -- 4.3 Folding Numbers -- 4.4 Some Mathematical Tidbits -- 4.5 General Folding Procedures -- 4.6 The Quasi-Order Theorem -- 4.7 Appendix: A Little Solid Geometry -- 5 Quilts and Other Real-World Decorative Geometry -- 5.1 Quilts -- 5.2 Variations -- 5.3 Round and Round -- 5.4 Up the Wall -- 6 Pascal, Euler, Triangles, Windmills -- 6.1 Introduction: A Chance to Experiment -- 6.2 The Binomial Theorem -- 6.3 The Pascal Triangle and Windmill -- 6.4 The Pascal Flower and the Generalized Star of David -- 6.5 Eulerian Numbers and Weighted Sums -- 6.6 Even Deeper Mysteries -- 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 ?0 -- 7.5 Schrรถder and Bernstein -- 7.6 Cardinal Arithmetic -- 7.7 Even More Infinities? -- 8 An Introduction to the Mathematics of Fractal Geometry -- 8.1 Introduction to the Introduction: Whatโs Different About Our Approach -- 8.2 Intuitive Notion of Self-Similarity -- 8.3 The lรฉnt Map and the Logistic Map -- 8.4 Some More Sophisticated Material -- An Introduction to the Mathematics of Fractal Geometry -- 8.1 Introduction to the Introduction: Whatโs Different About Our Approach -- 8.2 Intuitive Notion of Self-Similarity -- 8.3 The tent Map and and the Logistic Map -- 8.4 Some more Sophisticated Material -- 9 Some of Our Own Reflections -- 9.1 General Principles -- 9.2 Specific Principles -- 9.3 Appendix: Principles of Mathematical Pedagogy