Mathematics Galore!: Masterclasses, Workshops and Team Projects in Mathematics and Its ApplicationsThis book is a series of self-contained workshops in mathematics which aim to enthuse and inspire young people, their parents and teachers with the joy and excitement of modern mathematics. Written in an informal style, each chapter describes how novel mathematical ideas relate directly to real life. The chapters contain both a description of the mathematics and its applications together with problem sheets, their solutions and ideas for further work, project and field trips. Topics include; mazes, folk dancing, sundials, magic, castles, codes, number systems, and slide rules. This book should be accessible to young people from age thirteen upwards and yet contains material which should stretch the brightest students. |
Contents
Where we start | 10 |
How does a masterclass work? | 10 |
What is this book all about? | 10 |
The classes | 10 |
Acknowledgments | 10 |
Amazing mazes | 10 |
13 The mathematics of the Cretan Labyrinth | 11 |
14 The rise of the maze | 15 |
52 Early fortifications circles and the isoperimetric theorem | 127 |
53 Medieval castles | 137 |
54 More recent fortifications | 142 |
55 How to defend a castle | 145 |
56 Exercises | 151 |
57 Further problems | 153 |
58 Answers | 159 |
59 Mathematical notes | 162 |
15 How to solve a maze with your hand on a hedge | 17 |
16 How to solve a maze with a little network topology | 21 |
17 How to solve a maze using a packet of peanuts and a bag of crisps | 27 |
18 Modern mazes | 28 |
19 Exercises | 29 |
110 Further problems | 33 |
111 Answers | 35 |
112 Mathematical notes | 36 |
Dancing with mathematics | 38 |
22 Symmetry and group theory | 39 |
23 Back to dancing | 43 |
24 Bellringing and knitting | 48 |
25 Exercises | 51 |
26 Further problems | 53 |
27 Answers | 55 |
28 Mathematical notes | 60 |
29 References | 61 |
Sundials how to tell the time without a digital watch | 62 |
33 The motion of the sun | 64 |
34 The Equatorial sundial | 72 |
35 The horizontal sundial | 74 |
36 The vertical sundial | 79 |
37 The analemmatic sundial | 81 |
38 What time does a sundial show? | 85 |
39 Exercises | 92 |
310 Further problems | 94 |
311 Answers | 99 |
313 References | 100 |
Magical mathematics | 102 |
42 Magical mathematics | 103 |
43 Mathematical magic | 105 |
44 Conclusions | 115 |
46 Further problems | 117 |
47 Answers | 121 |
48 Mathematical notes | 123 |
49 References | 125 |
Castles mathematics in defence and attack | 126 |
510 References | 163 |
How to be a spy the mathematics of codes and ciphers | 165 |
62 What are codes and ciphers and what is the difference? | 168 |
63 The Caesar cipher | 169 |
64 Was Caesar a mathematician? | 171 |
65 Statistics and more general ciphers | 174 |
66 Multiple substitution ciphers | 177 |
67 Transposition ciphers | 181 |
68 Modernday ciphers | 184 |
69 Exercises | 185 |
610 Further problems | 187 |
611 Answers | 191 |
Some properties of the English language | 193 |
613 References | 194 |
Whats in a name? | 195 |
72 Number bases and base ten | 199 |
73 Other number bases | 202 |
74 The counting board | 207 |
75 Negative number bases | 208 |
76 Exercises | 212 |
77 Further problems | 215 |
78 Answers | 216 |
79 Mathematical notes | 218 |
710 References | 219 |
Doing the sums | 220 |
82 Before logarithms | 221 |
83 The life of John Napier | 222 |
84 What are logarithms? | 224 |
85 Using tables of logarithms | 228 |
86 The slide rule | 231 |
87 Who invented the slide rule? | 235 |
88 Exercises | 236 |
89 Answers | 241 |
810 Mathematical notes | 242 |
811 References | 244 |
| 249 | |
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Mathematics Galore!: Masterclasses, Workshops, and Team Projects in ... Christopher J. Budd,Christopher J. Sangwin No preview available - 2001 |
Common terms and phrases
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