Archimedes' modern works

Couverture......Page 1
Page de titre......Page 2
1. Comparison methods......Page 4
3. Organization of the book......Page 6
Historical Facts......Page 8
First Part: Archimedes Maps......Page 12
I. Introduction......Page 14
II. A direct extension of Archimedes' construction......Page 38
III. Comments......Page 39
II. The Archimedes-Lambert projection......Page 44
III. Archimedes Transformations and Archimedes Maps......Page 49
A. Optimal location of resources......Page 50
B. Optimal location of monitoring points......Page 51
2. Rotation......Page 52
B. The case of a square (or cube)......Page 54
A. General use......Page 55
B. Simple structures in two dimensions......Page 56
C. Analytic structures in higher dimensions......Page 60
D. Constructing an Archimedes Transform......Page 63
E. An explicit 3 dimensional example......Page 65
F. A general attempt for Archimedes Transform......Page 66
1. Archimedes Floating Bodies......Page 67
2. Building Archimedes Transforms......Page 69
G. An application: uniformly distributed points in a set......Page 70
Second Part: Archimedes "Method"......Page 74
Introduction......Page 76
I. Statement of the results......Page 80
II. Archimedes ideas and their evolution......Page 84
II. A direct application......Page 86
III.A first statement in modern terms......Page 88
IV. Enlarging the scope......Page 89
B. Modification of one of the solids......Page 90
V. A direct application to the cone......Page 91
VI. Cone and cylinder......Page 94
VII. The Method: Extended statement......Page 97
VIII. Four Dimensional Extension......Page 98
II. Weighing methods......Page 102
I. Introduction......Page 106
II. The robustness, extended statement......Page 107
A. Determination of the weight......Page 108
B. Finding the position of the center of gravity......Page 110
A. Hiero's crown......Page 111
B. What if the solid is not homogeneous?......Page 114
C. Using rotations......Page 115
1. Replacing any solid by an homogeneous one......Page 117
2. An invariant......Page 118
I. Introduction......Page 122
II. Basic results......Page 123
III. An estimate for the volume of a solid......Page 127
I. Introduction......Page 134
A. Description of the example......Page 135
C. Practical implementation......Page 137
A. Polynomials in one variable......Page 139
B. Case of a system of polynomial equations......Page 140
IV. Robustness of the method......Page 141
I. Introduction......Page 142
II. General approach......Page 143
A. The construction......Page 146
B. Using the ETRH for approximate computations......Page 149
C. Other similar hyperbolas......Page 150
D. Another approach......Page 152
IV. Generating artificial information......Page 154
V. Weights of solids......Page 160
A. Basic construction......Page 161
1. Uncertainty upon the refraction index......Page 164
3. Imprecise equality of moments......Page 165
II. Eddy Currents and Non Destructive Testing......Page 170
III. Archimedes comes in again......Page 173
Third Part: What is known about Archimedes?......Page 176
Introduction......Page 178
Plutarch......Page 182
Polybius......Page 187
Titus Livius......Page 191
Marcus Vitruvius Pollio......Page 193
Marcus Tullius Cicero......Page 195
Marcus Tullius Cicero......Page 196
The Tomb of Archimedes, modern times......Page 200
The modern siege of Syracuse......Page 203
2. Conceptualisation......Page 206
4. Technical abilities......Page 208
6. Modern views about Archimedes......Page 209
References......Page 211