Gardner, Martin: Mathematical Circus ©1968-1992 Martin Gardner Published by the Mathematical Association of America Hardcover, 273 pages ISBN 0883855062

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Contents: (for the most part the contents under the chapters are diagram listings, as the chapters are narrative and not made up of individual entries)

xi Preface (Don Knuth)
xiii Introduction (Martin Gardner)

3 Optical Illusions
6 Roger Hayward's "Undecidable" Monument
7 Puzzle Based on the Penrose Stairway
8 Possible Model for an Impossible Crate
9 The Nails That Stand Up
11 The Canadian Flag and Its Two Angry Men
12 A Gestalt Puzzle
12 Put the Bug Inside the Box
13 An Equal Distance Illusion
14 The Ghost Penny
14 Answers

16 Matches
17 The Piano Trick
18 Three Object Trick
20 Take Away Games
21 Hit And Run
24 Connecto
25 Seven Match Puzzles
27 Addendum
27 Answers

30 Spheres and Hyperspheres
33 Find the Radius of the Fourth Circle
36 Six Unit Circles Touch a Seventh
37 Twelve Unit Spheres Touch a Thirteenth
40 Four Circles Around One of Radius
41 Eight Unit Spheres Leave Room for One
42 Leo Moser's Hyperchessboard Problem
43 Answers

45 Patterns of Induction
47 Patterns for Sidney Sackson's Induction Game
48 How is this Pattern Ordered?
50 Three Stages in Probing for the Master Pattern
54 Addendum
55 Answers

56 Elegant Triangles
57 Joining the Centers of Three Equilateral Triangles
59 Centroid Trisects Medians
60 Trisecting Cevians
61 Smallest 5-Con Triangle Pair
63 Crossed Ladders Problem
64 Answers

66 Random Walks and Gambling
67 One Dimensional Random Walk with Absorbing Barriers
71 Symmetric Random Walk Based on the First 101 Digits of Pi
72 Paradox Based on a Random Walk Along a Line Without Barriers
74 Answers

75 Random Walks on the Plane and in Space
76 Random Walk on a Square Lattice
80 Ergodic Walk on a Square
82 Ergodic Random Walk on a Cube
84 Addendum
86 Answers

87 Boolean Algebra
89 George Boole
92 Venn Diagram for Set Intersection
93 Corresponding Symbols in Boolean Set Algebra & Propositional Calculus
95 Venn Diagram for Martini Puzzle
97 Circuits for Three Binary Relations
99 Answers

102 Can Machines Think?
103 A Turing Machine for Addition
110 Answers

111 Cyclic Numbers
112 Endless Strip for Prediction Trick
118 Addendum
121 Answers

123 Eccentric Chess and Other Problems
124 Talkative Eve
125 Three Squares
126 Pohl's Proposition
126 Escott's Sliding Blocks
127 Red, White, and Blue Weights
128 The 10-Digit Number
128 Bowling-Ball Pennies
129 Knockout Geography
130 Answers

137 Dominoes
138 The Standard Set of 28 Western Dominoes
141 Graphs for Solving the Row Problem With Complete Sets of Dominoes
143 A Sample Quadrille
145 Domino Magic Squares
147 Solving a Domino Grid Problem
150 Answers

152 Fibonacci and Lucas Numbers
153 Fibonacci
154 Tree Graph for Fibonacci's Rabbits
156 The First 40 Fibonacci and Lucas Numbers
158 Giant Sunflower with 55 Counterclockwise and 89 Clockwise Spirals
162 Computing Paths
165 Addendum
167 Answers

169 Simplicity
174 Measuring Simplity
176 A Simple Geometrical Theorem
177 A Combinatorial Problem
178 Addendum
180 Answers

182 The Rotating Round Table and Other Problems
182 Rotating Round Table
182 Single-Check Chess
183 Word Guessing Game
185 Triple Beer Rings
186 Two-Cube Calendar
186 Uncrossed Knight's Tours
188 Two Urn Problems
190 Ten Quickies
191 Answers

201 Solar System Oddities
211 Kepler's Model of the Solar System
213 Bode's Law for the Spacing of Planetary Orbits
214 Answers

216 Mascheroni Constructions
217 Bisect a Line with a Rusty Compass
220 Masheroni's Method Using a Compass Alone
221 How To Find a Circle's Center Using a Compass
224 Six Step Solution to Napoleon's Problem
225 Construct the Corners of a Square
226 Addendum
228 Answers

232 The Abacus
235 Abacist vs. Algorist
236 Chinese Suan Pan
237 Modern Japanese Soroban
238 A Russian Choty
241 Answers

242 Palindromes Words and Numbers
243 Flying Seagull - A Visual Palindrome
249 Doppelganger
250 Addendum
251 Answers

253 Dollar Bills
254 Inverting a Dollar Bill
255 Dollar Bill Poker
255 Royal Heath's Serial Number Divination
257 The Nine Principle
258 Ben Braude's Serial Number Trick
259 Using a Bill as a Ruler
260 Series of Puzzles
260 Answers

263 Postsript
269 Bibliography