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E-grāmata: Adventures In Recreational Mathematics (In 2 Volumes)

(London South Bank Univ, Uk)
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Adventures In Recreational Mathematics (In 2 Volumes)Palielināt
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David Singmaster believes in the presentation and teaching of mathematics as recreation. When the Rubik's Cube took off in 1978, based on thinly disguised mathematics, he became seriously interested in mathematical puzzles which would provide mental stimulation for students and professional mathematicians. He has not only published the standard mathematical solution for the Rubik's cube still in use today, but he has also become the de facto scribe and noted chronicler of the recreational mathematics puzzles themselves.Dr Singmaster is also an ongoing lecturer of recreational mathematics around the globe, a noted mechanical puzzle collector, owner of thousands of books related to recreational mathematical puzzles and the 'go to' source for the history of individual mathematical puzzles.This set of two books provides readers with an adventure into previously unknown origins of ancient puzzles, which could be traced back to their Medieval, Chinese, Arabic and Indian sources. The puzzles are fully described, many with illustrations, adding interest to their history and relevance to contemporary mathematical concepts. These are musings of a respected historian of recreational mathematics.
Volume 1 Adventures in Recreational Mathematics
Preface ix
About the Author xiii
1 What is Recreational Mathematics?
1(8)
Bibliography
7(2)
Part I Ancient Puzzles
9(154)
2 Puzzles from The Greek Anthology
11(6)
2.1 The Problems
12(3)
2.2 Solutions and Comments
15(1)
Bibliography
16(1)
3 Aryabhata and Other Early Indian Mathematicians
17(20)
3.1 Pythagorean Recreations
18(10)
3.2 Knowing What Each Pair Has
28(3)
3.3 The Snail in the Well
31(3)
Bibliography
34(3)
4 Alcuin and his Propositiones
37(48)
4.1 Alcuin
38(3)
4.2 The Manuscripts
41(2)
4.3 Managing the Text of Propositiones
43(2)
4.4 An Annotated Translation of Propositiones
45(30)
4.5 Summary and Discussions
75(7)
Bibliography
82(3)
5 The Problems of Abbot Albert
85(16)
5.1 Summary
100(1)
Bibliography
100(1)
6 Pacioli: The First Book of Mathematical Puzzles
101(30)
6.1 De Viribus Quantitatis
106(3)
6.2 Recreational Material in De Viribus Quantitatis
109(20)
Bibliography
129(2)
7 Pacioli's Magic and Card Tricks
131(8)
Bibliography
137(2)
8 Some Early Topological Puzzles
139(24)
8.1 The Chinese Wallet or Flick-Flack or Jacob's Ladder
140(3)
8.2 The Alliance and Victoria Puzzle
143(1)
8.3 Solomon's Seal or African Beads Puzzle
144(2)
8.4 The Cherries Puzzle
146(3)
8.5 Six-Piece Burrs
149(2)
8.6 Borromean Rings
151(2)
8.7 Chinese Rings
153(1)
8.8 Puzzle Grills
154(2)
8.9 Conclusions
156(1)
Bibliography
156(2)
Interlude: Finding a Sardinian Maze
158(5)
Part II New Ideas about Old Puzzles
163(2)
9 A Legacy of Camels
165(1)
9.1 Some History
166(4)
9.2 Analysis of the 17 Camels Problem
170(4)
9.3 Analysis of the 13 Camels Problem
174(5)
Bibliography
179(4)
10 Heronian Triangles
183(6)
10.1 Determination of Pythagorean triples
184(1)
10.2 Determination of Heronian triples
185(2)
Bibliography
187(2)
11 The Ass and Mule Problem
189(8)
11.1 Analysis of the Original Problem
190(1)
11.2 Doslic's Variation
191(2)
11.3 Another Simpler Variation
193(2)
Bibliography
195(2)
12 How to Count Your Chickens
197(14)
12.1 Answers
209(1)
Bibliography
210(1)
13 The Monkey and the Coconuts
211(24)
13.1 Determinate Versions
212(6)
13.2 Indeterminate Versions
218(6)
13.3 A General Solution
224(6)
13.4 Other Variations
230(2)
13.5 Solutions and Some Comments
232(1)
Bibliography
233(2)
14 Two River Crossing Problems
235(20)
14.1 De Fontenay's Generalization
237(3)
14.2 Dudeney's Solution
240(1)
14.3 Improved Solutions
241(3)
14.4 Proof of Optimality
244(5)
14.5 Missionaries and Cannibals
249(2)
14.6 Other Cultures
251(1)
Bibliography
252(3)
15 Sharing Barrels
255(14)
15.1 The Barrels Problem
256(1)
15.2 Integral Triangles
256(1)
15.3 Triangular Coordinates
257(1)
15.4 The Number of Integral Triangles
258(1)
15.5 The Number of Incongruent Integral Triangles
259(1)
15.6 Relation to Partitions
260(2)
15.7 Other Versions
262(3)
15.8 Fair Division of the First kn Integers into k Parts
265(2)
Bibliography
267(2)
16 Vanishing Area Paradoxes
269(5)
16.1 Early Examples
274(4)
Bibliography
278(3)
Appendix A Ancient and Important Sources 281(1)
A.1 Bibliography of Early Work 281(14)
A.2 Sources Project 295(2)
A.3 Open Problems 297
Volume 2 Adventures in Recreational Mathematics
Preface xi
About the Author xiii
1 Why Recreational Mathematics?
1(28)
1.1 The Nature of Recreational Mathematics
1(2)
1.2 The Utility of Recreational Mathematics
3(1)
1.3 Some Examples of Useful Recreational Mathematics
4(8)
1.4 Recreational Mathematics with Objects
12(2)
1.5 Examples of Medieval Problems
14(3)
1.6 Examples of Modern Recreational Problems
17(3)
1.7 The Educational Value of Recreations
20(4)
1.8 Why Is Recreational Mathematics So Useful?
24(1)
Bibliography
25(4)
2 On Round Pegs in Square Holes and Vice Versa
29(12)
2.1 Extremal Spheres
32(1)
2.2 Popular Conceptions
33(3)
2.3 Educational Value
36(3)
2.4 Appendix
39(1)
Bibliography
40(1)
3 Hunting for Bears
41(6)
3.1 The Square Path Version
42(3)
Bibliography
45(2)
4 Sum = Product Sequences
47(4)
Bibliography
50(1)
5 A Cubical Path Puzzle
51(8)
5.1 The Original Puzzle
51(4)
5.2 Further Problems
55(2)
Bibliography
57(2)
6 Recurring Binomial Coefficients
59(10)
6.1 Recurring Binomial Coefficients and Fibonacci Numbers
60(5)
6.2 Computer Search
65(2)
Bibliography
67(2)
7 Sums of Squares and Pyramidal Numbers
69(6)
Bibliography
73(2)
8 The Bridges of Konigsberg
75(14)
8.1 The Envelope Problem
80(2)
8.2 The Pregel Bridges
82(4)
8.3 Other Places
86(1)
Bibliography
87(2)
9 Triangles with Doubled Angles
89(18)
9.1 Geometry
89(6)
9.2 Diophantine Analysis
95(10)
Bibliography
105(2)
10 Quasicrystals and the University
107(6)
Bibliography
110(3)
11 The Wobbler
113(12)
11.1 The Height of the Center of Gravity
113(4)
11.2 The Distance Between Contacts
117(1)
11.3 Some Problems
117(2)
11.4 Paul Schatz's Oloid
119(2)
11.5 Other Results
121(2)
Bibliography
123(2)
12 Calculating for Fun
125(28)
12.1 The Chessboard Reward
125(4)
12.2 The Landowner's Earth and Air
129(3)
12.3 Buying Manhattan
132(6)
12.4 "It's a Hard Rain a Gonna Fall!"
138(1)
12.5 Permutations and the Number of Crosswords
139(3)
12.6 Grains of Sand versus Stars in the Sky
142(1)
12.7 "A Lottery is a Tax on the Innumerate."
143(1)
12.8 Storing a Million Pounds
144(1)
12.9 A4 Paper
144(3)
12.10 Other Exercises
147(3)
Bibliography
150(3)
13 Three Rabbits or Twelve Horses
153
13.1 The Three Rabbits Puzzle
153(4)
13.2 Four Horses, Twelve Horses and Other Puzzles
157(7)
Bibliography
164
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