The Mathematics of Oz
Mental Gymnastics from Beyond the Edge

Clifford A. Pickover

Cambridge University Press, 2002


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Grab a pencil. Relax. Then take off on a mind-boggling journey to the ultimate frontier of math, mind, and meaning as acclaimed author Dr Clifford Pickover, Dorothy, and Dr Oz explore some of the oddest and quirkiest highways and byways of the numerically obsessed. Prepare yourself for a shattering odyssey as The Mathematics of Oz unlocks the doors of your imagination. The thought-provoking mysteries, puzzles, and problems range from zebra numbers and circular primes to Legionĺs number - a number so big that it makes a trillion pale in comparison. The strange mazes, bizarre consequences, and dizzying arrays of logic problems will entertain people at all levels of mathematical sophistication.

The tests devised by enigmatic Dr Oz to assess human intelligence will tease the brain of even the most avid puzzle fan. Test your wits on a host of mathematical topics: geometry and mazes, sequences, series, sets, arrangements, probability and misdirection, number theory, arithmetic, and even several problems dealing with the physical world. With numerous illustrations, this is an original, fun-filled, and thoroughly unique introduction to numbers and their role in creativity, computers, games, practical research, and absurd adventures that teeter on the edge of logic and insanity. The Mathematics of Oz will have you squirming in frustration and begging for more.

Table of Contents

Travel Guide
Preface
Introduction
1. The Yellow-brick Road
2. Animal Array
3. An Experiment with Kansas
4. An Experiment with Signs
5. The Logic of Greenness
6. Magical Maze
7. Kansas Railway Contraction
8. The Problem of the Bones
9. Square Overdrive
10. Squares and Cubes
11. Plex's Matrix
12. Chaos at the Clock Factory
13. The Upsilon Configuration
14. Bone Toss
15. Animal Farm Courthouse
16. Omega Sphere
17. Leg Bone Shatter Produces Triangle
18. Z-Bar Ranch
19. Mystery of Phasers
20. Salty Number Cycle
21. Where are the Composites? 
22. Brain Trip
23. The Gaps of Omicron
24. Hutchinson Problem
25. Flint Hill Series
26. Wacky Tiles
27. Toto Clone Puzzle
28. Legions' Number
29. The Problem of the Tombs
30. Plex's Tiles
31. Phasers on Targets
32. The Chamber of Death and Despair
33. Zebra Irrationals
34. Creatures in Resin
35. Prime-poor Equations
36. Number Satellite
37. Flatworm Math
38. Regolith Paradox
39. ˧§ˇˇˇ§§§§
40. Entropy
41. Animal Gap
42. Arranging Alien Heads
43. Ramanujan Congruences and the Quest for Transcendence
44. Getting Noticed
45. Juggler Numbers
46. Friends from Mars
47. Phi in Four 4s
48. On Planet Zyph
49. The Jellyfish of Europa
50. Archeological Dissection
51. The Gamma Gambit
52. Robot Hand Hive
53. Ramanujan and the Quattuordecillion
54. Lunatic Ferris Wheel
55. The Ultimate Spindle
56. Prairie Artifact
57. Alien Pellets
58. The Beauty of Polygon Slicing
59. Cosmic Call
60. Knight Moves
61. Sphere
62. Potawatomi Target
63. Sliders
64. Swapping
65. Triangle Dissection
66. A Simple Code
67. Heterosquare
68. Insertion
69. Missing Landscape
70. The Choice
71. Animal Selection
72. The Skeletal Men of Uranus
73. Hindbrain Stimulation
74. The Arrays of Absolution	
75. Trochophore Abduction
76. The Dream Pyramids of Missouri
77. Mathematical Flower Petal
78. Blood and Water
79. Cavern Problem
80.  Three Triplets
81. Oos and Oob Gambit
82. Napiform Mathematics
83. Toto, Mr. Plex, Elephant
84. Witch Overdrive
85. What is Art?
86. Wendy Magic Square
87. Heaven and Hell
88. The Stars of Heaven
89. Vacation in the Tarantula Nebula
90. Hot Lava
91. Circular Primes
92. The Truth About Cats and Dogs
93.  Disc Mania
94.  N2+m2=s
95. 2, 271, 2718281
96. Android Watch
97. Knight Moves	
98. Pool Table Gambit
99.  A Connection Between Pi  and e
100. Venusian Number Bush
101. Triangle Cave
102. Rat Attack
103. The Scarecrow Formula
104. Circle Math
105. A, AB, ABA
106. Ants and Cheese
107. The Omega Crystal
108. Attack of the Undulating Undecamorphs
Epilog
Further Exploring
For Further Reading

Index

The index will give you more ideas about some of the topics covered.
antimagic squares, 324
augmented primes, 330

blood and water, 166
bones, 21-22, 34-35, 40-41
Borwein, Peter, 284-285
Brill, Bob, 325

Caldwell, Chris, 272-274
Champernowne's number, 283-284
cheese, 223
circles, 25, 219-220, 341
circular primes, 190-191, 330
clocks, 29-30
composite numbers, 49-50, 79-82, 263
congruneces, Ramanujan, 97-100
Connell numbers, 88-89, 294
Continued fractions, 284
Cookson Hills series, 268
Copeland-Erd÷s constant, 284
cosine law, 256-257
Crump, Joe, 250
cubes, 26

De Geest, Patrick, 330
Descartes, RenÚ, 341
Devlin, Keith, 330
Dockery, Daniel, 290
Drake, Frank, 59
Dubner, Harvey, 273
Dumas, Stephane, 135-137
Dutil, Yvan, 135-137

e (number) 206-208, 289, 321, 333, 337-338
Earls, Jason, 278, 287, 338
entropy, 90-92
Euler, Leonard, 289
EulerNet project, 251
exclusionary squares, 251
expected value, 244

Factorial, 65
	primes, 272
Farris, Frank, 125-126, 311
ferris wheel, 124-125
Fibonacci numbers, 45-46, 261, 339
flatworm math, 84-85
Flint Hills Series, 57-58
fractals, 220, 286, 342

Gaps of Omicron, 53-54
Gauss, Carl, 262
geometry, 5, 10, 21, 34, 38, 40, 42, 53, 109, 115,
  124, 127, 132, 140, 146, 176, 186, 199, 217, 219, 223
God's formula, 206
golden ratio, 109-110, 305
googol, 123
greenness, 15-16

Hailstone numbers, 103, 304
harmonic mean, 246
heterosquares, 149-150

insect senses, 301
irrational numbers, 74, 250, 277
Israel, Robert, 278

J÷rgenson, Loki, 284-285
Juggler numbers, 102-105

knight moves, 138-139, 201-203

Lakhtakia, Akhlesh, 294
law of cosines, 256-257
leaning bricks, 236-237
Legion's Number, 64-65
lissajous curves, 176-178, 324-325

magic squares, 150, 173, 183, 325, 327
mazes, 17-18, 29, 32, 36, 51, 55, 81, 107, 113,
    119, 138, 174, 184, 201, 204, 211, 214
mean value, 243
mean, harmonic, 246
Meyerson, Mark, 128, 313
Meyrignac, Jean-Charles, 252

number theory, 100, 109, 330
numbers, Legion's, 64-65
	Champernowne's, 283-284
	composite, 49-50,79-82
	Connell, 88-89, 294
	Copeland-Erd÷s, 284
	cube, 24
	Fibonacci, 45-46, 261
	Hailstone, 103
	irrational, 74, 250, 277
	Juggler, 102-105
	obstinate, 330
	polygonal, 226-228
	polymorphic, 344-346
	prime, 79-82, 190-191, 289-290, 315, 327, 330
	rational, 249, 265
	square, 24-26
	transcendental, 250
	visualizing, 285-286
	Zebra, 74-75
	
obstinate numbers, 330
omega sphere, 38-39
omega crystal, 225
omicron gaps, 53-54
Ono, Ken, 297
partitions, 94-95
permutable primes, 330
phasers, 44-45
phi, 109-110, 305
physical world, 5, 10, 19, 90,101,102,166, 214
pi, 206-208, 266, 277, 284-285, 332-333, 337-338
Plank, Darrell, 248, 265, 267, 272
polygon slicing, 132-134
polygonal numbers, 226-228
polymorphic numbers, 344-346
Pool table, 204-206
Poonen, Bjorn,134
prime numbers, 79-82, 190-191, 289-290, 315, 327, 330
	augmented, 330
	circular, 190-191, 330
	factorial, 272
	permutable, 330
	theorem, 262
	primorial, 273
	twin, 263
Primorial, primes, 273
probability, 71, 70, 189, 261, 276, 318,  321, 329

railway, 19-20 
Ramanujan congruences, 97-100
Ramanujan formula, 310
random variable, 244
rational numbers, 249, 265
rats, 214-216
root mean square, 246
Rubinstein, Michael, 134
Rumplestilskin sequence, 287

Sagan, Carl, 277
scarecrow formula, 217-218
sequences, 88
	Rumplestilskin, 287
series 57-58, 225,265-266, 344
	geometric, 260
Sery, Robert, 290
SETI, 135-137
sieve of Eratosthenes, 262
signals (alien), 135-137
signs, 13-14
Smith, Harry, 282, 302-303, 332
sphere, Omega, 38-39
sphere problem, 140
spindle, 127-128
squares, 24-27
	exclusionary, 251
	tridigital, 250
Squarion, 25
Stong, Robert, 249

tetrahedron, 268
tombs, 66
transcendental numbers, 250
triangle inequality theorem, 259
triangles, 40-41, 146-147, 218, 259, 319
tridigital squares, 250
twin primes, 263

undecamorphs, 226-228
undulation, 226-228, 338
upsilon configuration, 32-33

visualizing numbers, 285-286

Weaver, Rhiannon, 297

yellow-brick road, 5-6

zebra numbers, 74-75