**Dolciani Mathematical Expositions**

Volume: 33;
2008;
375 pp;
Hardcover

**Print ISBN: 978-0-88385-339-9
Product Code: DOL/33**

List Price: $63.00

AMS Member Price: $47.25

MAA Member Price: $47.25

**Electronic ISBN: 978-1-61444-207-3
Product Code: DOL/33.E**

List Price: $63.00

AMS Member Price: $47.25

MAA Member Price: $47.25

# Sink or Float?: Thought Problems in Math and Physics

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*Keith Kendig*

MAA Press: An Imprint of the American Mathematical Society

Sink or Float: Thought Problems in Math and Physics is a collection of problems drawn from mathematics and the real world. Its multiple-choice format forces the reader to become actively involved in deciding upon the answer. The book's aim is to show just how much can be learned by using everyday common sense. The problems are all concrete and understandable by nearly anyone, meaning that not only will students become caught up in some of the questions, but professional mathematicians, too, will easily get hooked. The more than 250 questions cover a wide swath of classical math and physics. Each problem s solution, with explanation, appears in the answer section at the end of the book. A notable feature is the generous sprinkling of boxes appearing throughout the text. These contain historical asides or little-known facts. The problems themselves can easily turn into serious debate-starters, and the book will find a natural home in the classroom.

#### Reviews & Endorsements

This book is well written and easy to understand and little is required in the way of a mathematical background. The challenging problems will interest both beginning students and those with a strong mathematical background. Readability is enhanced by over 210 figures and nearly 70 notes which contain historical and related facts. Recommended.

-- D. P. Turner, Choice

# Table of Contents

## Sink or Float?: Thought Problems in Math and Physics

Table of Contents pages: 1 2

- cover cover11
- copyright page ii3
- Title page iii4
- Preface vii8
- Contents xiii14
- What Do You Think? A Sampler 116
- Geometry 924
- Introduction 924
- Archimedean Spirals 1227
- Spiral Length 1328
- Church Window 1429
- Church Window Again 1530
- Mastic Spreader 1631
- Elliptical Driveway 1732
- Perpendicular at Both Ends 1732
- Star Area 1833
- Stereo Camera 1934
- Diagonals of a Parallelogram 2035
- Half and Half? 2136
- Half and Half Again 2136
- A Platonic Solid 2237
- A Chip Off the Old Block 2338
- Pyramid Volumes 2338
- Ring-Shaped Fishing Weight 2439
- Largest Cylinder in a Sphere 2540
- Largest Cone in a Sphere 2540
- Spin It Again! 2641
- Solid Angles of a Tetrahedron 2742
- A Right Turn 2843
- A Limit | or Chaos? 2944
- What About Areas? 2944
- A Glass Skeleton 3045
- Adding a Room 3146

- Numbers 3348
- A Curious Property 3550
- Multiplication from Another Era 3550
- How Often Does Lightning Strike? 3651
- A Never-Ending Decimal 3752
- What is This? 3752
- A Wild Sequence 3752
- Body-Builder 3853
- Decimal versus Binary 3853
- Hexadecimal versus Binary 3954
- Gelosia Again 3954
- Do Their Behaviors Correspond? 4055
- Ingenious Student 4156
- Gain or Lose? 4257
- What Sort of Graph? 4257
- Round Trip 4257
- A Reality Test 4358
- Friday the 13th Again 4459
- Friday the 13th One More Time 4459
- What Comes Next? 4459

- Astronomy 4560
- Introduction 4560
- Which Way? 5065
- Our Spinning Moon 5065
- How High is High Noon? 5166
- Flagpole Sundial 5166
- The Greatest Number of Stars 5166
- Is This Possible? 5166
- Sunspots 5267
- Not a Plumb Plumb 5267
- Foucault's Pendulum 5368
- Attaching the Wire 5570
- A Lunar Foucault Pendulum? 5671
- Retrograde Motion? 5671
- Moonday 5772
- Full Moon 5772
- Full Moon, Again 5873
- Moondial 5873
- Moonrise 5873
- Moonstruck? 5873
- Earth's Phases 5873
- Opening or Closing Parenthesis? 5974
- Light Lumps, Massive Spheres 5974
- Dynamite Asteroids 5974
- Impact Angle 6075
- A Manned ``Deep Impact'' Mission? 6176
- Vaporizing Asteroid 6277
- Vernal Equinox 6378
- Martian Equinox? 6378
- An Ancient ``Aha!'' 6378

- Archimedes' Principle 6782
- Introduction 6782
- A solution to th 7085
- Another Way? 7186
- Rain Gauge 7186
- Beachball 7287
- Top versus Bottom 7388
- Pouring Buckshot 7489
- Wooden Spheres 7489
- Hot Buckshot 7590
- Hot Buckshot Melts Through 7691
- Air Pocket 7792
- Melting Ice Cube 7893
- Float Capacity 7994
- Arctic Blast 8095
- A Tale of Two Boats 8398

- Probability 85100
- Introduction 85100
- Red and White 94109
- Red, White and Blue 94109
- Dropped Penny 94109
- What are the Chances? 95110
- Teachers versus Students 95110
- Exit Polls 95110
- Ideal Tetrahedron 95110
- Sex and Money 96111
- Three Children 96111
- Average Distance 96111
- Short Sticks 96111
- Average Distance-Squared 97112
- High-Noon Shadows 97112
- How Grim the Reaper? 98113
- Can You Trust This Headline? 98113
- Common Birthdays 98113
- A Serious Waiting Game 99114
- A Random-Integer Game 99114
- Bottles versus Boxes 100115
- Throwing Darts 101116
- Monte Carlo 101116
- Monte Carlo and Average Distance 103118
- Monte Carlo and the Needle Toss 103118
- Short Sticks Revisited 103118

- Classical Mechanics 105120
- Introduction 105120
- How Much Work? 109124
- Toy Car 109124
- Grandfather Clock 110125
- Gravity's Horsepower 110125
- Spinning Turntable 110125
- A Running Start 111126
- Squeezing the Earth 111126
- Galileo's Cannonball 112127
- Muzzle-Speed 113128
- Muzzle-Speed, Again 113128
- Muzzle-Speed, One More Time 113128
- Greatest Range 114129
- Pulling Strings 115130
- Where Does the Arrow Land? 115130
- A Buoyancy Machine 116131
- On the Moon 117132
- Have You Heard of This? 117132
- Now What Will Happen? 119134
- Twanging Rod 120135
- Total Torque 121136
- Saturn's Rings 122137

- Electricity and Magnetism 123138
- Introduction 123138
- Classical Mechanics vs. Electricity 130145
- Staying Power 131146
- Survivors 132147
- A Current Difference? 133148
- Later 133148
- Voltage Change 133148
- Current Difference, Again 134149
- Type AA 134149
- Most Massive 135150
- A Question of Polarity 136151
- A Coil Around a Coil 137152
- A Fatter Wire 138153
- Forgetting to Turn It Off 138153
- Building a Large Magnet 138153
- A Larger Capacitor 139154
- More Turns 139154
- Warm Resistors 140155
- Four Charges 141156
- Energy Loss 141156
- The Shrinking Capacitor 142157

- Heat and Wave Phenomena 143158
- Introduction 143158
- A Cooling Rod Problem 150165
- How Hot is Hottest? 151166
- Does the Peak Walk? 151166
- Going to Zero 152167
- How Far? 152167
- Hefty Block, Wimpy Spring 153168
- Spring Stiffness 154169
- Spring Stiffness, Again 154169
- Switching Off Gravity 155170
- Method versus Madness 156171
- A Ceiling Under Stress 158173
- Adding Waves 159174
- Losing Energy 160175
- Losing Energy, Again 161176
- Friction and Frequency 161176
- Going, Going, Gone! 162177

Table of Contents pages: 1 2