CONTENTS
5. Light billiards, anti-stealth-boats and egoist mirrors 104
6. The perfect display cupboard 106
7. The way from the right angle 108
8. Platonic beauties 110
9. Christmas chaos 111
10. Circle inversions 112
11. A new universe 113
12. To infinity, and beyond 116
13. Reading and surfing tips 118
Part 3. Current Topics 121
Chapter 9. The Role of Mathematics in the Financial Markets
Walter Schachermayer 123
References 133
Chapter 10. Electronic Money:
An Impossibility or Already a Reality?
Albrecht Beutelspacher 135
1. Introduction 135
2. What is money? 135
3. Cryptographic mechanisms 136
4. Electronic money: the basic scheme 138
5. Double spending 139
6. Extra properties 140
Summary 141
References 141
Chapter 11. Spheres in the Computer—the Kepler Conjecture
Martin Henk and Gunter
¨
M. Ziegler 143
A really hard nut 143
In the plane 145
Into the third dimension 152
A scandalous situation 156
A recipe? 157
Computer versus Kepler 161
Problems, problems 161
References 163
Chapter 12. How Do Quanta Compute?
The New World of the Quantum Computer
Ehrhard Behrends 165
1. Why are prime numbers important in cryptography? 166
2. A mathematical preparation: period lengths 167
3. Some quantum mechanics 168
4. Qbits: the components of a quantum computer 170
5. How does one factorize large numbers with a quantum computer? 171
6. Summary 173
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