Index
Adams, S. , 28 4
Aigner, M. , 27 0
algebraic integer , 22 8
algebraic numbe r o f degre e d , 215
approximation exponent , 221, 230, 23 7
auxiliary polynomial , 223 , 22 5
badly approximabl e irrationa l number , 214
Banach, S. , 282 , 29 0
Banach-Tarski paradox , 280 , 282 , 290 , 29 6
strong for m of , 293 , 29 5
Bender, E . A. , 171
Beukers, F. , 23 6
Bezout's Theorem , 108
Birch an d Swinnerton-Dye r conjecture , 11 9
Blichfeldt's Lemma , 170
Boltianskii, V . G. , 270 , 30 2
Bolyai, F. , 25 7
Bolyai-Gerwien theorem , 29 7
Borsuk's conjecture , 298 , 30 7
for a smoot h conve x body , 30 7
in M
2,
30 1
i n R 3 , 30 5
Borsuk's problem , 298 , 30 0
for a smoot h conve x body , 30 7
i n R
2
, 30 1
in M
3,
30 5
canonical form , 3 3
Type 0 , 3 4
Type 1, 3 4
Type 2 , 3 4
Type 3 , 3 4
Cantor, G. , 22 0
Cappell, S . E. , 192
Caratheodory's theorem , 29 9
Chahal, J . S. , 101
chord an d tangent , 8 7
Cipra, B. , 30 9
congruent number , 47 , 90 , 9 4
problem, 4 7
convex body , 30 0
strictly convex , 30 7
convex pol y tope, 186
Dehn, M. , 27 0
invariant, 27 0
Diaz, R. , 192
Dickson, L . E. , 9 0
dihedral grou p D 8, 10, 33 , 144
dilation, 5 6
Diophantine equation , 233 , 23 5
Diophantus, 87 , 197
Dirichlet's Approximatio n Theorem , 161,
196, 20 5
Dirichlet's Theorem , 115
dissection
reflexivity of , 25 1
symmetry of , 25 1
transitivity o f fo r conve x polygons , 25 3
Dubins, L. , 29 8
Dyson, F. , 22 1
Eggleston, H . G. , 298 , 30 6
Ehrhart, E. , 168
polynomial, 190
Theorem of , 185, 186
elliptic curve , 101, 103, 112-114
group o f L- valued point s of , 109, 111
L-valued point s of , 104
equicomplementability, 25 8
equidecomposability, 280 , 281, 29 6
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