شگفتی‌های ریاضی برای الهام‌بخشی به معلمان و دانش‌آموزان: برای الهام‌بخشی به معلمان و دانش‌آموزان

Are you "proud" to admit that you never liked math? Were never good in math? Are you struggling to pique your students' interest in math? Are you bored by the routine, mechanical aspects of teaching to the test in mathematics? This book offers a plethora of ideas to enrich your instruction and helps you to explore the intrinsic beauty of math. Through dozens of examples from arithmetic, algebra, geometry, and probability, Alfred S. Posamentier reveals the amazing symmetries, patterns, processes, paradoxes, and surprises that await students and teachers who look beyond the rote to discover wonders that have fascinated generations of great thinkers. Using the guided examples, help students explore the many marvels of math, including The Amazing Number 1,089 . Follow the instructions to reverse threedigit numbers, subtract them, and continue until everyone winds up with . . . 1,089! The Pigeonhole Principle . All students know that guesstimating works sometimes, but now they can use this strategy to solve problems. The Beautiful Magic Square . Challenge students to create their own magic squares and then discover the properties of Dürer's Magic Square. The author presents examples to entice students (and teachers) to study mathematicsto make mathematics a popular subject, not one to dread or avoid. Cover Page......Page 1 Title Page......Page 2 ISBN 0871207753......Page 3 CONTENTS......Page 6 Foreword......Page 10 Preface......Page 13 1 The Beauty in Numbers......Page 18 1.1 Surprising Number Patterns I......Page 19 1.2 Surprising Number Patterns II......Page 22 1.3 Surprising Number Patterns III......Page 23 1.4 Surprising Number Patterns IV......Page 24 1.5 Surprising Number Patterns V......Page 26 1.7 Amazing Power Relationships......Page 27 1.8 Beautiful Number Relationships......Page 29 1.9 Unusual Number Relationships......Page 30 1.10 Strange Equalities......Page 31 1.11 The Amazing Number 1,089......Page 32 1.12 The Irrepressible Number 1......Page 37 1.13 Perfect Numbers......Page 39 1.14 Friendly Numbers......Page 41 1.16 Palindromic Numbers......Page 43 1.17 Fun with Figurate Numbers......Page 46 1.18 The Fabulous Fibonacci Numbers......Page 49 1.19 Getting into an Endless Loop......Page 52 1.20 A Power Loop......Page 53 1.21 A Factorial Loop......Page 56 1.22 The Irrationality of √2......Page 58 1.23 Sums of Consecutive Integers......Page 61 2 Some Arithmetic Marvels......Page 64 2.1 Multiplying by 11......Page 65 2.2 When Is a Number Divisible by 11?......Page 66 2.3 When Is a Number Divisible by 3 or 9?......Page 68 2.4 Divisibility by Prime Numbers......Page 69 2.5 The Russian Peasant’s Method of Multiplication......Page 74 2.6 Speed Multiplying by 21, 31, 41......Page 76 2.7 Clever Addition......Page 77 2.8 Alphametics......Page 78 2.9 Howlers......Page 81 2.10 The Unusual Number 9......Page 86 2.11 Successive Percentages......Page 89 2.12 Are Averages Averages?......Page 91 2.13 The Rule of 72......Page 92 2.14 Extracting a Square Root......Page 94 3 Problems with Surprising Solutions......Page 96 3.1 Thoughtful Reasoning......Page 97 3.2 Surprising Solution......Page 98 3.3 A Juicy Problem......Page 99 3.4 Working Backward......Page 101 3.5 Logical Thinking......Page 102 3.6 It’s Just How You Organize the Data......Page 103 3.7 Focusing on the Right Information......Page 105 3.8 The Pigeonhole Principle......Page 106 3.9 The Flight of the Bumblebee......Page 107 3.10 Relating Concentric Circles......Page 109 3.11 Don’t Overlook the Obvious......Page 110 3.12 Deceptively Difficult (Easy)......Page 112 3.13 The Worst Case Scenario......Page 114 4 Algebraic Entertainments......Page 115 4.1 Using Algebra to Establish Arithmetic Shortcuts......Page 116 4.2 The Mysterious Number 22......Page 117 4.3Justifying an Oddity......Page 118 4.4 Using Algebra for Number Theory......Page 120 4.5 Finding Patterns Among Figurate Numbers......Page 121 4.6 Using a Pattern to Find the Sum of a Series......Page 125 4.7 Geometric View of Algebra......Page 126 4.8 Some Algebra of the Golden Section......Page 129 4.9 When Algebra Is Not Helpful......Page 132 4.10 Rationalizing a Denominator......Page 133 4.11 Pythagorean Triples......Page 134 5 Geometric Wonders......Page 140 5.1 Angle Sum of a Triangle......Page 141 5.2 Pentagram Angles......Page 143 5.3 Some Mind-Bogglers on......Page 148 5.4 The Ever-Present Parallelogram......Page 150 5.5 Comparing Areas and Perimeters......Page 154 5.6 How Eratosthenes Measured the Earth......Page 156 5.7 Surprising Rope Around the Earth......Page 158 5.8 Lunes and Triangles......Page 160 5.9 The Ever-Present Equilateral Triangle......Page 163 5.10 Napoleon’s Theorem......Page 166 5.11 The Golden Rectangle......Page 170 5.12 The Golden Section Constructed by Paper Folding......Page 175 5.13 The Regular Pentagon That Isn’t......Page 178 5.14 Pappus’s Invariant......Page 180 5.15 Pascal’s Invariant......Page 182 5.16 Brianchon’s Ingenius Extension of Pascal’s Idea......Page 185 5.17 A Simple Proof of the Pythagorean Theorem......Page 187 5.18 Folding the Pythagorean Theorem......Page 189 5.19 President Garfield’s Contribution to Mathematics......Page 191 5.20 What Is the Area of a Circle?......Page 193 5.21 A Unique Placement of Two Triangles......Page 195 5.22 A Point of Invariant Distance in an Equilateral Triangle......Page 197 5.23 The Nine-Point Circle......Page 200 5.24 Simson’s Invariant......Page 204 5.25 Ceva’s Very Helpful Relationship......Page 206 5.26 An Obvious Concurrency?......Page 210 5.27 Euler’s Polyhedra......Page 212 6 Mathematical Paradoxes......Page 215 6.1 Are All Numbers Equal?......Page 216 6.2 −1 Is Not Equal to +1......Page 217 6.3 Thou Shalt Not Divide by 0......Page 218 6.4 All Triangles Are Isosceles......Page 219 6.5 An Infinite-Series Fallacy......Page 223 6.6 The Deceptive Border......Page 225 6.7 Puzzling Paradoxes......Page 227 6.8 A Trigonometric Fallacy......Page 228 6.9 Limits with Understanding......Page 230 7 Counting and Probability......Page 232 7.1 Friday the 13th!......Page 233 7.2 ThinkBefor e Counting......Page 234 7.3 The Worthless Increase......Page 236 7.4 Birthday Matches......Page 237 7.5 Calendar Peculiarities......Page 240 7.6 The Monty Hall Problem......Page 241 7.7 Anticipating Heads and Tails......Page 245 8 Mathematical Potpourri......Page 246 8.1 Perfection in Mathematics......Page 247 8.2 The Beautiful Magic Square......Page 249 8.3 Unsolved Problems......Page 253 8.4 An Unexpected Result......Page 256 8.5 Mathematics in Nature......Page 258 8.6 The Hands of a Clock......Page 264 8.7 Where in the World Are You?......Page 268 8.8 Crossing the Bridges......Page 270 8.9 The Most Misunderstood Average......Page 273 8.10 The Pascal Triangle......Page 276 8.11 It’s All Relative......Page 280 8.12 Generalizations Require Proof......Page 281 8.13 A Beautiful Curve∗......Page 282 Epilogue......Page 285 Acknowledgments......Page 288 Index......Page 289 About the Author......Page 293 If you like this book, you’ll LOVE the membership!......Page 295

Are you "proud" to admit that you never liked math? Were never good in math? Are you struggling to pique your students' interest in math? Are you bored by the routine, mechanical aspects of teaching to the test in mathematics?

This book offers a plethora of ideas to enrich your instruction and helps you to explore the intrinsic beauty of math. Through dozens of examples from arithmetic, algebra, geometry, and probability, Alfred S. Posamentier reveals the amazing symmetries, patterns, processes, paradoxes, and surprises that await students and teachers who look beyond the rote to discover wonders that have fascinated generations of great thinkers. Using the guided examples, help students explore the many marvels of math, including

* The Amazing Number 1, 089. Follow the instructions to reverse three-digit numbers, subtract them, and continue until everyone winds up with... 1, 089!
* The Pigeonhole Principle. All students know that guesstimating works sometimes, but now they can use this strategy to solve problems.
* The Beautiful Magic Square. Challenge students to create their own magic squares and then discover the properties of Dürer's Magic Square.

The author presents examples to entice students (and teachers) to study mathematics--to make mathematics a popular subject, not one to dread or avoid.

Note: This product listing is for the Adobe Acrobat (PDF) version of the book.

SNAP Bronze Award Winner! Engaging students in math lessons and encouraging them to explore math principles is much easier-and lots more fun-when you use this book's amazing collection of quirks, illustrations, problems, and surprises. Dazzle your students with Peculiar number patterns and properties Clever shortcuts and tricks for avoiding cumbersome mathematic processes Curious problems that reveal problem-solving strategies Algebra problems that shed light on patterns in mathematics and the behavior of numbers Activities and demonstrations that uncover timeless geometric principles Used as attention-getters, motivators, or enrichment activities, these math wonders leave students questioning and exploring further, regardless of their grade level or ability. This book offers ideas to enrich instruction and help teachers explore the intrinsic beauty of math. Through dozens of examples from arithmetic, algebra, geometry, and probability, the symmetries, patterns, processes, paradoxes, and surprises that have facilitated generations of great thinkers are revealed. Activities include: (1) The Beauty in Numbers; (2) Some Arithmetic Marvels; (3) Problems with Surprising Solutions; (4) Algebraic Entertainments; (5) Geometric Wonders; (6) Mathematical Paradoxes; (7) Counting and Probability; and (8) Mathematical Potpourri. (KHR) Recieved item on time, right when we were told it would arrive. Book in very good condition.