Games and Mathematics (47 page)

Tani
,
Y.
(
1964
)
The Magic Calculator: the Way of the Abacus
,
Japan Publications Trading Company
.

Tartakower
,
S. G.
(
1956
)
My Best Games of Chess 1931–1954
, ed.
H.
Golombek
,
G. Bell & Sons
.

Thurston
,
W.
(
1994
)
Proof and progress in mathematics
,
Bulletin of the American Mathematical Society
,
30–7
,
161
–177, reprinted in
For the Learning of Mathematics
, 15–1, Feb. 1995.

Turkle
,
S.
&
Papert
,
S.
(
1990
)
Epistemological pluralism: styles and voices within the computer culture
,
Signs
,
16–1
,
128
–157. Reprinted in
Humanistic Mathematics Network Journal
, 7, 1992, 48–9, 51.

Turner
,
J. C.
&
van de Griend
,
P.
(
1996
)
History and Science of Knots
,
World Scientific
.

Tylor
,
E. B.
(
1879
)
The history of games
,
The Fortnightly Review
,
25
,
735
–747. Reprinted in Avedon & Sutton-Smith 1971, 63–76.

Van Binsberge
,
W.
(n.d.) Board-games and divination in global cultural history, shikanda.net/ancient_models/gen3/mankala/mankala1.htm.

Villegas
,
F. R.
(
2007
)
Experimental Number Theory
,
Oxford University Press
.

Voltaire
(
1764
)
A Philosophical Dictionary
. Walsh, D.,
The probability of a tie in three candidate race
,
http://frank.mtsu.edu/-dwalsh/3votetie.gif
[retrieved 28 Oct. 2009].

Weisstein
,
E. W.
(
2006
) Hofstadter-Conway $10,000 Sequence, MathWorld, mathworld.wolfram.com.

Wells
,
D. G.
(
1976
)
Guerilla
,
boardgame
,
Ariel, UK
.

Wells
,
D. G.
(
1979
)
Checkpoint: Danger
boardgame, Ideal in USA and (as Galaxis, in 1980) by
Ravensburger in Germany
.

Wells
,
D. G.
(
1979
)
Recreations in Logic
,
Dover
.

Wells
,
D. G.
(
1980
–1983),
The Problem Solver
, 8 issues.

Wells
,
D. G.
(
1982
–1984)
Can You Solve These?
(Books 1, 2 & 3)
Tarquin Publications
.

Wells
,
D. G.
(
1986
/1998)
The Penguin Dictionary of Curious and Interesting Numbers
(1st edn. 1986, 2nd revised edn. 1998).

Wells
,
D. G.
(
1987
)
Mathematics through Problem Solving
,
Blackwell
. Re-edited and republished as
Problem Solving for National Curriculum Mathematics
Blackwell, (1990).

Wells
,
D. G.
(
1988
)
Hidden Connections, Double Meanings
,
Cambridge University Press
.

Wells
,
D. G.
(
1988
)
Which is the most beautiful?
The Mathematical Intelligencer
,
10–4
,
30
–1.

Wells
,
D. G.
(
1990
)
Are these the most beautiful?
The Mathematical Intelligencer
,
12–3
,
37
–41.

Wells
,
D. G.
(
1991
a)
The Penguin Dictionary of Curious and Interesting Geometry
,
Penguin
.

Wells
,
D. G.
(
1991
b) Games as a metaphor for mathematics, Discussion Group on the Philosophy of Mathematics, British Congress of Mathematics Education, convened by Paul Ernest, 13--16 July 1991.

Wells
,
D. G.
(
1992
)
Penguin Book of Curious and Interesting Puzzles
,
Penguin
, reprinted,
Dover
, 2006, as
Book of Curious and Interesting Puzzles
.

Wells
,
D. G.
(
1993
a) Problem Solving and Investigations, 3rd edition, Rain Press.

Wells
,
D. G.
(
1993
b) When is a problem solved?, Workshop on how Mathematicians Work, HMW Group,
Bulletin of the Institute of Mathematics and its Applications
,
29
,
24
–26.

Wells
,
D. G.
(
1995
)
You are a Mathematician: a Wise and Witty Introduction to the Joy of Numbers
,
Penguin
(and Wiley 1997).

Wells
,
D. G.
(
1997
)
The Penguin Book of Curious and Interesting Mathematics
,
Penguin
.

Wells
,
D. G.
(
2003
)
The End of Civilisation: Science, Ideology and Irrationality
,
Rain Press
.

Wells
,
D. G.
(
2005
)
Prime Numbers
,
Wiley
.

Wells
,
D. G.
(
2008
)
What's the Point? Motivation and the Mathematics Crisis
, Rain Press.

Wells
,
D. G.
(
2010
)
Philosophy and Abstract Games
,
Rain Press
.

Wells
,
D. G.
&
Clarke
,
S.
(
1988
)
What's the point of games in the mathematics classroom?
Investigator
,
12
.

Wells
,
D. G.
&
Schultz
,
D
. (
2008
)
A surprise with parallel Lines: an exploration that went wrong, then right
,
The Mathematical Gazette
,
92
,
162
–164.

Weyl
,
H.
(
1995
)
Topology and abstract algebra as two roads of mathematical comprehension
, Parts 1 & 2,
American Mathematical Monthly
,
102–5
& 102–7; translation by Abe Shenitzer of
Unterrichtsblätter für Mathematik und Naturwissenschaften
, (1932), 38,
177
–188.

Wigner
,
E. P.
(
1960
) The unreasonable effectiveness of mathematics in the natural sciences,
Communications in Pure and Applied Mathematics
,
13--1
, Wiley.

Williams
,
H. C.
(
1998
)
Éduard Lucas and Primality Testing
,
John Wiley
.

Williams
,
H. C.
&
Shallit
,
J. O.
(
1994
) Factoring integers before computers, in Gautschi 1994.

Wilson
,
R. J.
(
1985
) Analysis situs, in Alavi
et al
., 1985, pp. 789–800.

Wolfenstein
,
M.
(
1958
) The emergence of fun morality, in E. Larrabee and R. Meyersohn, eds.,
Mass Leisure
, Free Press, pp.
86
–97.

Yan
,
L.
&
Shiran
,
D.
(
1987
)
Chinese Mathematics: a Concise History
,
Clarendon Press
.

Young
,
W. H.
(
1928
)
The mathematical method and its limitations
,
Atti del Congresso Internazionale Dei Matematici
,
Bologna
, 3–10 September 1928, vol. 1 of 6. N. Zanichelli, Bologna, 1929.

Zeilberger
,
D.
(
1993
)
Theorems for a price: Tomorrow's semi-rigorous mathematical culture
,
Notices of the American Mathematical Society
,
40–8
,
978
–981.

21-point cubic
128

85 Ways to Tie a Tie
,
The
21

Alcuin of York
3

d’Alembert, Jean le Rond
75
,
150

Alexander, C. H. O’D.
51

Alekhine, Alexander
210

d’Ambrosio, Ubiritan
225

annotations
46

Apobates
218
,
219

Apollonius of Perga
88
,
93
,
149
,
159

Appel, K. I. & Haken, W.
145

Archimedes
108
,
123
,
133

Archimedes’ lemma
171

Argand, Jean Robert
201

Aristotle
166
,
217
,
218
,
221

Atiyah, Michael
120
,
152
,
226

Bacon, Francis
214

Bailey, David
143
,
147

Bailey-Borwein-Plouffe formula
147

Bakshali manuscript
4

bell ringing
218

Berlekamp, Elwyn
38
,
62

Berne, Eric
218

Bernoulli, James
112

Bieberbach, Ludwig
226

billiards
164–165

Binsberge, Wim van
222–223

Bishop, Alan
227

bishop path puzzle
33

blind mathematicians
41

Boas, Ralph
51

Board Game Studies
57

Boorman, Scott
45

Borwein brothers
136
,
142

Borwein, Jonathan
143
,
147

Bourbaki
214
,
227
,
228

Bouton, Charles
38

Brahe, Tycho
149

braids
2
,
233

Bridges of Königsberg
9–11
,
43
,
56
,
61

Brilliancy (Beauty) prize
210

Brocard, Henri
126

Bronstein, David
51

Brouwer's fixed point theorem
28

Browne, Cameron
29

Buckyball
223–224

Bunimovich stadium
166

Cake-Cutting Algorithms
21

calculating prodigies
142

Cardan, Gerolamo
136

Catoptrica
163

Cavalieri, B. F.
153

Cayley, Arthur
119

Ceva, Giovanni
88–89

Chen, Master
173

chess
29–35
,
52–53

chess, blindfold
16

Chinese mathematics
35

Chinese dissections
172

Clarke, Shirley
48–49

Coates, Roger
99

Cohn-Vossen
51

Combinatorial Game Theory
38–39

Commentary on the Nine Chapters
173

Community of the Future, The
31

competition
54

Constable, John
189

Conway, John Horton
37
,
38
,
55

Copernicus, Nicolaus
149

Cuisennaire rods
75
,
77

Culin, Stewart
222

cycloid
160

Dandelin's spheres
93–94

Davis, P. J.
123
,
127

Deep Blue
37

Descartes, René
65
,
115
,
143
,
157
,
159
,
160
,
190

Dido, Queen of Carthage
168–169

Dieudonné, Jean
58
,
171

Dirac, Paul
232

divergent series
49
,
111

divisor function
79–80

Dudeney, Henry Ernest
24
,
71

Dyson, Freeman
214

Egypt
1
,
3

Eight Queens puzzle
23

Einstein, Albert
31
,
85
,
148
,
150

Emergence of Fun Morality, The
222

enri
calculus
161

Epstein, D.
143

Erastosthenes’ sieve
64
,
133–134
,
197

Erdös, Paul
228

ethnomathematics
225

Euclid
49
,
75
,
90
,
93
,
134
,
227

Euclid,
Elements
49
,
85
,
98
,
169

Euler, Leonhard
9–15
,
40
,
61
,
65
,
73
,
75
,
84
,
99
,
110
,
111–114
,
126
,
131
,
138
,
142
,
169
,
213
,
215
,
226

Euler line of triangle
123–125
,
128

Euler's constant
113

Euler's relation for polyhedra
115–116
,
224

Euwe, Max
47

Everybody's Illustrated Book of Puzzles
11

Exemplum memorabile inducionis fallacis
138

Experimental Mathematics
(journal)
143

Experimental Mathematics
(book)
147

Fatou dust
212

Fermat, Pierre de
155–156
,
157
,
159
,
167
,
207
,
213

Fermat's Last Theorem
46
,
55
,
162

Feuerbach, K. W.
126

Fibonacci
3
,
54

Fibonnaci sequence
131

Fine, Reuben
230

Fink, Thomas
21

Fisher, M. E.
71

four-colour theorem
144–145

Frege, Gotlob
73

Gale, David
28

Galileo
50
,
60
,
148
,
157

game (gamen)
219

Game of Letter-Board
76

Game of Life, The
37
,
55

Games People Play
218

Gamow, George
52

Gasser, Ralph
26

Gauss, Carl Friedrich
84
,
114
,
131
,
140
,
142
,
143
,
177
,
197
,
226
,
233

Geometria Indivisibilibus
153

Geometry and the Imagination
51

Go
35–39

Go Proverbs Illustrated
52

Goldbach's theorem
135–136

Golomb, Solomon
23–24

Goodtsein, R. L.
76

Grandi, Guido
112

Greek mathematics
2
,
60
,
96
,
126
,
127
,
148
,
150

Gregory, James
109–110

groups
119
,
218

Grundy, Patrick
38

Guy, Richard
38
,
57