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Hayes D.F. (ed.), Shubin T. (ed.) Ч Mathematical Adventures for Students and Amateurs
Hayes D.F. (ed.), Shubin T. (ed.) Ч Mathematical Adventures for Students and Amateurs

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Ќазвание: Mathematical Adventures for Students and Amateurs

јвторы: Hayes D.F. (ed.), Shubin T. (ed.)

јннотаци€:

How should you encode a message to an extraterrestrial? What do frogs and powers of 2 have in common? How many faces does the Stella Octangula have? Is a plane figure of constant diameter a circle, and what has this to do with NASA? 210 = 5 x 6 x 7 = 14 x 15, so just how many numbers can be the product of both two and of three consecutive integers? Is there any such thing as a truly correct map? What patterns are possible in juggling?

What do all of these questions have in common? They, and many others, are answered in this book.

The authors are distinguished mathematicians; some are bright newcomers while others have been well known in mathematical circles for decades.

This is a partial record of the Bay Area Math Adventures (BAMA), a lecture series for high school students (and incidentally their teachers, parents, and other interested adults) hosted by San Jose State and Santa Clara Universities in the San Francisco Bay Area. These lectures are aimed primarily at bright high school students, the emphasis on bright, and as a result, the mathematics in some cases is far from what one would expect to see in talks at this level. There are
serious mathematical issues addressed here.

We hope that this book will capture some of the magic of these talks that have filled auditoriums at the host schools almost monthly for several years. Join the students in sharing these mathematical adventures.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2004

 оличество страниц: 304

ƒобавлена в каталог: 11.04.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Abel, Niels Henrik      246 257
Ahlfors' "five islands" theorem      255
Ahlfors, Lars V.      255Ч257
Aleksandrov, A.D.      214
Alexanderson, Gerald L.      34
Algebraic integer      58
Analytic continuation      78
Appel, Kenneth      17
Archimedes      219 221Ч225 227 228 230 231
Arecibo Message      5
Aristaeus      219
Armstrong, Neil      9
Asymptote      168 174 181 191 231 275
Babylonians      53 54 164
Banach's matchbox problem      145
Banach, Stefan      145 146
Bayesian probability distribution      139 153
Benford's law      47
Berra, Yogi      27
Bertrand's paradox      150 151
Beukers, Frits      61
Bijection      91 101 103 108 109 111 116 see
Binary operation      168
Binet formulas      97
Binomial coefficient      106 107 110
Birch and Swinnerton Ч Dyer conjecture      61 78Ч80
Birthday problem      138
Bloch's constant      254 256
Bloch's principle      254
Bloch's theorem      254Ч56
Bloch, Andre      254 257
Boethius      52
Bonk and Eremenko theorem      256
Bonk, Mario      256 257
Boole, George      278
Brianchon's theorem      173 174 179Ч183
Bryant, Robert      7
Buffon Needle Problem      138 149 153
Cardioid      186
Carroll, Lewis      259 261 271 275 278 280 see
Cartan Ч Hadamard theorem      202Ч203 208 211 212
Cartan Ч Hadamard Ч Gromov theorem      208
Cauchy Ч Riemann equations      246Ч248
Centroid      221 223 228Ч231
Challenger (Space shuttle)      7 10 11 16
Check digit      27 33 34 38
Chromatic polynomial      114 116
Coates and Wiles theorem      79
Coates, John H.      79 80
Cole, Frank Nelson      20
Collinear      165 166 168 173Ч176 178Ч182
Complex cosine      253
complex derivative      247 248
Complex exponential      248 250
Complex function      247 248 250 252 255
Complex logarithm      249 250 254
Complex number      78 246Ч248 250 251
Complex plane      246Ч248 251 252
Complex sine      253
Complex variable      78 233 251
Conformality      233 244Ч246 248Ч250 252Ч256
Conic section      157 165 166 181
Conjecture      74
Connolly, Robert      144 145
Contractibility      205Ч208 211 212
Convergence      56 78 136 138 247 248
Convex polygon      120 171
Convex polyhedron      120 121
Copernicus, Nicolaus      38
Coprime      58
Coram, Marc      152 153
Cubical complex      202 209Ч211 214
cuboid      51 61 62
Curvature      201 202 205 206 257
Curvature, Gaussian      201 202 206 209
Curvature, nonpositive      202Ч212 214 215
Curve of constant width      11 13 see
Cusp      185Ч189 191 194 197 198
Cycloid      185 188
D'Alembert, Jean le Rond      247
Darwin, Charles      38
de Fermat, Pierre      74
de Morgan, Augustus      269 278
De Morgan, William      269
Defect      253
Degree of a polynomial equation      246
density      44 143 152 186 197 219 221Ч225 227Ч231 252
Desargues' theorem      173 175Ч177 183
Developable surface      250
Diaconis, Perci      139 153
Differential      244 245 248 256
Directed ratio      173
DNA      5
dodecahedron      120 122Ч124 128Ч132
Dodgson, Charles Lutwidge      259Ч262 265 267Ч280 see
Doyle, Peter      116
Drake's equation      6
Drake, Frank      4 6
Dual statement      180
Duality      122
Egyptians, ancient      157
Eilenberg Ч MacLane theorem      212
Einstein, Albert      38 51
ellipse      165 166 181 186Ч189 191 241Ч243 250 256
Elliptic curve      60 61 63 65 66 69 71 73 75Ч77 79 80 253
Enigma code      17
Equidistribution      44Ч48
Eremenko, Alexandre      256 257
Error, correction      32
Error, detection      27 33 38
Euclid      121 184 219 259 272Ч275 279
Euclid's Elements      273
Euclidean distance      203 204 209
Euclidean geometry      183 184
Euclidean plane      204 208 247
Euclidean space      209
Euclidean triangle      204Ч206 210
Eudoxus      273
Euler's theorem      234 236 250
Euler, Leonhard      20 53 58 60 62 63 234 247 257
Evolute      186 187 191
Extended complex plane      252
Fake circle      11 14Ч16 see
Feller, William      141 144 153
Fermat's last theorem      25 61 65
Feynman, Richard      9 10 16
Fields medal      255
Flat torus      206Ч209 214
Four Vertex Theorem      187
Four-color theorem      17 18 25 114 267
Freshman sum      84
Freudenthal, Hans      3 6
Function, analytic      247 248 252Ч255
Function, complex      247 248 250 252 255
Function, entire      247 248 251Ч255
Function, linear      158Ч160
Function, meromorphic      251Ч257
Function, multiple-valued      250
Function, rational      251 252
Fundamental theorem of algebra      247 248 250 251
Galilei, Galileo      38
Gallian, Kristin      32
Gardner, Martin      136 144 153
Gauss' theorema egregium      250
Gauss, Carl Friedrich      55 56 246 247 250 257
Generator      166 212Ч214
Geodesic path      203Ч206 208Ч210
Geodesic space      203 205Ч209 212Ч214
Gladstone, William Ewart      274
Graham, Ronald L.      44
Graph      114Ч116
Graph, coloring      114 115
Graph, incomparability      114 115
Greeks, ancient      19 51 52
Gromov's lemma      211 214
Gromov, Mikhail L.      214
Group      67 69 105 116 122 123 128 131 202 203 211Ч215
Group presentation      212Ч214
Group, abelian      67 69 105 116
Group, finitely-generated      69
Group, fundamental      202 203 211Ч215
Group, homology      214 215
Group, symmetric      105
Group, symmetry      122 123 128 131 212
Haken, Wolfgang      17
Hall, Marshall      105 116
Halley, Edmund      245 257
Harmonia Mundi      126
Harrison, George      33
Hasse, Helmut      78
Heath, Thomas L.      219 231
Hexahedron (cube)      120 122 123 125 128
Homeomorphism      201 202 206 215
Homothety (simple scaling)      243
Homotopy      201 202 205 207 208 211 212 214
Huxley, Thomas      30
Hyperbola      166 168 174 181
icosahedron      117 120 122 123 128 131Ч133
Independent identically distributed sequence (HD)      141 142
Induction, mathematical      110 133 163
Infinite product      78
Infinite series      247
Invariant      201 202 214 219
inversion      180 182 183
Isometry      202 207 208
Isomorphic groups      211Ч214
Kepler, Johannes      126
Klein bottle      214
Klimek, Paul      99
Knuth, Donald      31 39 44
L-function      78
Lagrange, Joseph      247
Lambert's map      239 240 242 243 256
Lambert, Johann      234 257
Laplace, Pierre Simon      136 141
Law of Large Numbers      136
Legendre, Adrien Marie      273 274
Lennon, John      27 32 36
Liddell, Alice Pleasance      259 261 279
LINCOS      3 4 6
Line at infinity      168 176 177 181
Linear, approximation      244
Linear, equation      18 157 158 275 276
Linear, extension      114 115
Linear, function      158Ч160
Linear, map      241 244
Linear, order      115
Linear, recurrence      97 98
Linear, transformation      241 243 244 256
Link of a vertex      210 211 214
Magnusson, Bengt      99 103
MapleЩ      18
Markov chain      98 142
Mathemagician      83
MathematicaЃ      18Ч20
McAuliffe, Christa      7 9
McCartney, Paul      27
McNair, Ron      7 9
Menelaus' theorem      173Ч175 178 179 183
Mercator map (projection)      233 235 237Ч240 243Ч245 249 250
Mercator, Gerhardus      233 235 237 239 256
Mersenne Prime Search      20
Mersenne, Marin      19 20
Metric      207
Moebius inversion      111
Moebius strip      214 266
Monte Carlo simulation      149
Monty Hall problem      136
Mordell, Louis      65 69 71
National Aeronautics and Space Administration (NASA)      11 14Ч16
Needham, Tristan      250 257
Nevanlinna's theorem      253 255
Nevanlinna, Rolf      252 253 255Ч257
Newton's method      157 163 165
Newton, Sir Isaac      38
Non-Euclidean geometry      183 184
Number, complex      78 246Ч248 250 251
Number, congruent      73Ч75 77Ч79
Number, Eulerian      108 110 111
Number, harmonic      54Ч57 59 60
Number, irrational      41 42 44 46Ч48 97
Number, perfect      20 21
Number, prime      3Ч6 19Ч25 58 70 77 78
Number, rational      41 42 47 48 54 69 73Ч75
Number, triangular      52 54 55 59 60
Numbers, Fibonacci      83Ч85 89 90 92 97 98
Numbers, Gibonacci      92 96 97
Numbers, Lucas      89Ч92 96Ч98
O-ring      9 10
octahedron      120 122 123 126Ч128 132
One-to-one correspondence      87 88 94 101 107 111 112 see
Order relation      114
Pappus' theorem      173Ч175 182 183
parabola      160 166Ч168 181 185 219Ч221 227Ч231
Paraboloid      219 221 222 225 229Ч231
Partial order      114 115
Partially ordered set      99 113 see
Pascal's theorem      157 162 165 166 168 173 174 178 180Ч183
Pascal's triangle      106 110 111
Pascal, Blaise      166
Pasteur, Louis      38
Patashnik, Oren      44 116
Peirce, Benjamin      273
Permutation      99 101Ч116
Permutation, cyclic      103 111
Permutation, descent of      108Ч110 112 113 115 116
Picard's theorems      251Ч255
Picard, Emile      251 252 257
Picasso, Pablo      194 195
Pigeonhole Principle      41 42 44 47 48
Plimpton collection      54
Poincare disk      204 205
Point at infinity      65 66 168 176 251Ч253
Point, inflection      66 191
Point, integer      70 71
Point, rational      54 61Ч63 69 71 75Ч79
Poisson process      143
Pole      251 252
Polya, George      28 39 48
Polyhedron      16 117 120Ч124 132 133
Poncelet Ч Brianchon theorem      173 174 181Ч183
POSET      99 100 111 113Ч116 see
Power of point theorem      178
Power series      78 247 248 251
Price, Bartholomew      259 268 269 271 273Ч277 279
Prime      19Ч21 25
Prime factorization      19Ч23 25 58
Projection      152 166Ч168 181 197Ч199 207 208 235Ч240 242Ч245 249Ч253 256
Projection, covering      207 208
Projection, cylindrical      235Ч240 243 245 249
Projection, plate carree      239 240 242 256
Projection, stereographic      245 249Ч253 256
Projective 2Чspace      66
Projective geometry      66 168 175 176 181 183
Projective plane      168 176 181 265
Projective transformation      166 176 183
Pythagoras      51Ч54 63
Pythagorean cuboid      61 62
Pythagorean Theorem      53 73
Pythagorean triple      54 61 62
1 2
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