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Adventures In Recreational Mathematics - Volume Ii [Pehme köide]

(London South Bank Univ, Uk)
Teised raamatud teemal:
Teised raamatud teemal:
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.
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(5)
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(2)
Bibliography
40(1)
3 Hunting for Bears
41(6)
3.1 The Square Path Version
42(5)
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(4)
Bibliography
57(2)
6 Recurring Binomial Coefficients
59(10)
6.1 Recurring Binomial Coefficients and Fibonacci Numbers
60(5)
6.2 Computer Search
65(4)
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(3)
Bibliography
87(2)
9 Triangles with Doubled Angles
89(18)
9.1 Geometry
89(6)
9.2 Diophantine Analysis
95(12)
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(4)
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(6)
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
Bibliography
164