Eureka!: Math Fun from Many Angles

199 Pages·1983·4.58 MB·English

by  David Lewis

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Author's Note _____________
The name EUREKA is taken from a charming bit of bath
ematics. More than 2000 years ago, the King of Greece asked
the famous mathematician Archimedes to determine if
his crown were pure gold or alloyed with silver. While
lounging in the tub, Archimedes realized that a crown of
pure gold would displace more water than an equal volume
of lighter alloyed gold. So enthralled was he by this dis
covery that he ran naked through the streets of Syracuse,
shouting, "Eureka! I've got it!"
Well, I hope you receive the same pleasure from reading
this book that Archimedes got from solving his problem or
that I got from writing it. You might even want to read it
in the bathtub.
My thanks go to my sister Emily, who contributed the
subtitle. I would also like to thank my agent Betty Marks
and editor Paul Heacock. I am also indebted to Miriam
Smith and Mary Secor and the other mem bers of the
Onteora staff who were instrumental in the creation and
writing of Eureka!
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Errata _________________________________ _
1. There are no mistakes in this book. The above should
read "ERRATUM."
Is the correction a mistake or not?

Contents
1l~ Fun and Games
1. Twisted Topology 15
2. A Bag of Tricks and Treats 26
3. A Score of Games 36
4. The Magic's There 48
5. Rubiquity 60
~~ Nifty Numerics
6. Palindromesemordnilap 69
7. A Pole Vaulter 71
8. A Timely Switch 73
3)~ Fallacies and Logic
9. If This Is Not a Chapter, My Name Is
Raymond Smullyan 75
10. Thrice Befuddled 89
11. Better Mixed-Up Than Lost 92
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~g And Even Dissection of Solids
12. Archimedes Anderson and the Case of the
Sinister Plot 93
13. How to Dissect a Square and Other Marvels
of Modern Biology 96
14. Geometer's Heaven 105
15. Hole in the Sphere 108
16. Convexstasy 110
17. Great Unsolved Problems 113
18. Out of This World 115
@g Photons Are Light Matter, Too
19. Archimedes Anderson and the Gambling
Candidate 119
20. Once Upon a Time. . . 122
21. A Problem Fly 123
22. The Leading Series of Pisa 124
23. The Early Something Catches the Whatever 127
®g Shortcuts
24. A Speedier System of Solving 129
25. A Letter Home 135
26. In Which We Are Initiated Into the Secret
Society of Square Root Solvers 137
27. Heads and Legs 141
28. Noble Bases 143
29. A Division in Ancient Rye 145
30. Getting at the Root of the Problem 146
31. Or is it 32? Remumbt:r Nembers 149
12 EUREKA!
'1h
Neat Numbers
32. Prime Time 151
33. A Sense of Balance 159
34. Perfect Numbers and Some Not-So-Perfect
Numbers 161
f8)~ Cranium Crackers and Cheese:
Problems to Munch On
35. Classy Problems 165
36. LEITERS + DIGITS = FRUSTRATION 174
~~ FUNdamental Ratios
37. Expand Your Mind 181
38. E? Ah! 183
39. A Section of Gold 188
40. A Bundled-Up Buyer 195
41. A Piece of Pi 196
Bibliography 202
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