Seduced by Mathematics: The Enduring Fascination of Mathematics

Description

Seduction is not just an end result, but a process — and in mathematics, both the end results and the process by which those end results are achieved are often charming and elegant. This helps to explain why so many people — not just those for whom math plays a key role in their day-to-day lives — have found mathematics so seductive. Math is unique among all subjects in that it contains end results of amazing insight and power, and lines of reasoning that are clever, charming, and elegant. This book is a collection of those results and lines of reasoning that make us say, "OMG, that's just amazing," — because that's what mathematics is to those who love it. In addition, some of the stories about mathematical discoveries and the people who discovered them are every bit as fascinating as the discoveries themselves. This book contains material capable of being appreciated by students in elementary school — as well as some material that will probably be new to even the more mathematically sophisticated. Most of the book can be easily understood by those whose only math courses are algebra and geometry, and who may have missed the magic, enchantment, and wonder that is the special province of mathematics. Contents Preface — Just What Does She See in Him, Anyway? About the Author Introduction: Seduced by Mathematics Seduced by Murder Mysteries The World Series (and Other Best of … Competitions) A Seductive Proof of the Pythagorean Theorem Bibliography Chapter 1 Seduced by Numbers Size Matters Prime Numbers Seductive Numbers 2 Algebraic Numbers π e Reciprocity Bibliography Chapter 2 Seduced by Arithmetic Last Digit Standing 1,729 635,318,657 Taxicab Numbers An Oldie But Goodie 1,089 Does the 1,089 Trick Work in Octal? 6,174 Beating the Averages in Investing Bibliography Chapter 3 Seduced by Patterns Recursive and Explicit (Formulaic) Patterns Fibonacci Numbers Excel 101 Fun with Fibonacci — Excel 102 More about the Golden Ratio The Quicksand of Mathematics Seduced by Hidden Patterns Last Marble in the Jar A Different Last Marble Problem Bibliography Chapter 4 Seduced by Analytic Geometry The Unexpected Parallelogram — Varignon’s Theorem Morley’s Theorem Covering Up Homage to the Greeks Descartes and the Birth of Analytic Geometry But It Doesn’t Just Make Geometry Easier Implicit Functions The Moving Dot Foxes and Rabbits — The Lotka–Volterra Equations Bibliography Chapter 5 Seduced by Mathematical Induction (and How to Avoid It) The Principle of Mathematical Induction March Madness, Classic Version The GOAT — Candidate #1 The Sum of Odd Integers The GOAT — Candidate #2 Bibliography Chapter 6 Seduced by Calculus I Simply the Best Crossing a River The L-Shaped Corridor Two You Don’t Often See Four Problems, One Diagram Bibliography Chapter 7 Seduced by Complex Numbers Rene Descartes’ Imaginary Contribution The Work of Man The Complex Plane Euler’s Formula De Moivre’s Theorem The nth Roots of 1 Partial Fractions Complex Numbers and Differential Equations A Cutie from Multivariable Calculus The Residue Theorem Bibliography Chapter 8 Seduced by Infinite Series Geometric Series Questions Tool #1 — The Thin Sub-sequence Test Torricelli’s Tower Taylor’s Theorem Playing with Infinite Series Offspring Riemann’s Casino John von Neumann and the Bumblebee Bibliography Chapter 9 Seduced by Probability Playing Games The Birthday Problem The Monty Hall Problem Bayes’ Theorem Tennis, Anyone? Tennish, Anyone? Entanglement in Quantum Mechanics Probabilistic Entanglement Blackwell’s Bet Bibliography Chapter 10 Seduced by Infinity Sleight of Hand One-to-One Correspondences Finite and Countable Sets: Hilbert’s Hotel An Influx of Bynars Cantor’s Theorem The Continuum Hypothesis The Axioms of Set Theory The Axiom of Choice Transfinite Induction Zorn’s Lemma Bibliography Chapter 11 Seduced by Computers Chaotic Phenomena The Traveling Salesman Problem Easy, Hard, and Nasty Problems Temple of Benares/Tower of Hanoi The Traveling Salesman Problem Returns Monte Carlo Simulations Making a Name for Yourself — with the Aid of a Computer and This Book Bibliography Chapter 12 Seduced by a Few of My Favorite Things My Favorite Mathematical Joke My Next Favorite Mathematical Joke One Good Whack To the Vector Belong the Spoils Equivalence Relations Mathematical Results with Amusing Names Fixed-Point Theorems Bibliography Index