Games and Mathematics (47 page)

Read Games and Mathematics Online

Authors: David Wells

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.
Index
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, 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 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 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

Other books

No Way Back by Matthew Klein
Tripping on Tears by Rusk, Day
The 50 Worst Terrorist Attacks by Edward Mickolus, Susan L. Simmons
Wednesday's Child by Alan Zendell
All She Ever Wanted by Lynn Austin
The Shepherd's Betrothal by Lynn A. Coleman
Whisper of Magic by Patricia Rice
Hunted by Riley Clifford