Math Wonders to Inspire Teachers and Students

by Posamentier, Alfred S.

• ISBN13: 9780871207753
• ISBN10: 0871207753
• Format: Paperback
• Copyright: 2003-04-01
• Publisher: Assn for Supervision & Curriculum

Table of Contents

Foreword	ix
Preface	xii
The Beauty in Numbers	1	(46)
Surprising Number Patterns I	2	(3)
Surprising Number Patterns II	5	(1)
Surprising Number Patterns III	6	(1)
Surprising Number Patterns IV	7	(2)
Surprising Number Patterns V	9	(1)
Surprising Number Patterns VI	10	(1)
Amazing Power Relationships	10	(2)
Beautiful Number Relationships	12	(1)
Unusual Number Relationships	13	(1)
Strange Equalities	14	(1)
The Amazing Number 1,089	15	(5)
The Irrepressible Number 1	20	(2)
Perfect Numbers	22	(2)
Friendly Numbers	24	(2)
Another Friendly Pair of Numbers	26	(1)
Palindromic Numbers	26	(3)
Fun with Figurate Numbers	29	(3)
The Fabulous Fibonacci Numbers	32	(3)
Getting into an Endless Loop	35	(1)
A Power Loop	36	(3)
A Factorial Loop	39	(2)
The Irrationality of √2	41	(3)
Sums of Consecutive Integers	44	(3)
Some Arithmetic Marvels	47	(32)
Multiplying by 11	48	(1)
When Is a Number Divisible by 11?	49	(2)
When Is a Number Divisible by 3 or 9?	51	(1)
Divisibility by Prime Numbers	52	(5)
The Russian Peasant's Method of Multiplication	57	(2)
Speed Multiplying by 21, 31, and 41	59	(1)
Clever Addition	60	(1)
Alphametics	61	(3)
Howlers	64	(5)
The Unusual Number 9	69	(3)
Successive Percentages	72	(2)
Are Averages Averages?	74	(1)
The Rule of 72	75	(2)
Extracting a Square Root	77	(2)
Problems with Surprising Solutions	79	(19)
Thoughtful Reasoning	80	(1)
Surprising Solution	81	(1)
A Juicy Problem	82	(2)
Working Backward	84	(1)
Logical Thinking	85	(1)
It's Just How You Organize the Data	86	(2)
Focusing on the Right Information	88	(1)
The Pigeonhole Principle	89	(1)
The Flight of the Bumblebee	90	(2)
Relating Concentric Circles	92	(1)
Don't Overlook the Obvious	93	(2)
Deceptively Difficult (Easy)	95	(2)
The Worst Case Scenario	97	(1)
Algebraic Entertainments	98	(25)
Using Algebra to Establish Arithmetic Shortcuts	99	(1)
The Mysterious Number 22	100	(1)
Justifying an Oddity	101	(2)
Using Algebra for Number Theory	103	(1)
Finding Patterns Among Figurate Numbers	104	(4)
Using a Pattern to Find the Sum of a Series	108	(1)
Geometric View of Algebra	109	(3)
Some Algebra of the Golden Section	112	(3)
When Algebra Is Not Helpful	115	(1)
Rationalizing a Denominator	116	(1)
Pythagorean Triples	117	(6)
Geometric Wonders	123	(75)
Angle Sum of a Triangle	124	(2)
Pentagram Angles	126	(5)
Some Mind-Bogglers on π	131	(2)
The Ever-Present Parallelogram	133	(4)
Comparing Areas and Perimeters	137	(2)
How Eratosthenes Measured the Earth	139	(2)
Surprising Rope Around the Earth	141	(2)
Lunes and Triangles	143	(3)
The Ever-Present Equilateral Triangle	146	(3)
Napoleon's Theorem	149	(4)
The Golden Rectangle	153	(5)
The Golden Section Constructed by Paper Folding	158	(3)
The Regular Pentagon That Isn't	161	(2)
Pappus's Invariant	163	(2)
Pascal's Invariant	165	(3)
Brianchon's Ingenius Extension of Pascal's Idea	168	(2)
A Simple Proof of the Pythagorean Theorem	170	(2)
Folding the Pythagorean Theorem	172	(2)
President Garfield's Contribution to Mathematics	174	(2)
What Is the Area of a Circle?	176	(2)
A Unique Placement of Two Triangles	178	(2)
A Point of Invariant Distance in an Equilateral Triangle	180	(3)
The Nine-Point Circle	183	(4)
Simson's Invariant	187	(2)
Ceva's Very Helpful Relationship	189	(4)
An Obvious Concurrency?	193	(2)
Euler's Polyhedra	195	(3)
Mathematical Paradoxes	198	(17)
Are All Numbers Equal?	199	(1)
-1 Is Not Equal to +1	200	(1)
Thou Shalt Not Divide by 0	201	(1)
All Triangles Are Isosceles	202	(4)
An Infinite-Series Fallacy	206	(2)
The Deceptive Border	208	(2)
Puzzling Paradoxes	210	(1)
A Trigonometric Fallacy	211	(2)
Limits with Understanding	213	(2)
Counting and Probability	215	(14)
Friday the 13th!	216	(1)
Think Before Counting	217	(2)
The Worthless Increase	219	(1)
Birthday Matches	220	(3)
Calendar Peculiarities	223	(1)
The Monty Hall Problem	224	(4)
Anticipating Heads and Tails	228	(1)
Mathematical Potpourri	229	(39)
Perfection in Mathematics	230	(2)
The Beautiful Magic Square	232	(4)
Unsolved Problems	236	(3)
An Unexpected Result	239	(2)
Mathematics in Nature	241	(6)
The Hands of a Clock	247	(4)
Where in the World Are You?	251	(2)
Crossing the Bridges	253	(3)
The Most Misunderstood Average	256	(3)
The Pascal Triangle	259	(4)
It's All Relative	263	(1)
Generalizations Require Proof	264	(1)
A Beautiful Curve	265	(3)
Epilogue	268	(3)
Acknowledgments	271	(1)
Index	272	(4)
About the Author	276