Stillwell J. — Yearning for the Impossible: The Surprising Truths of Mathematics :: Электронная библиотека попечительского совета мехмата МГУ

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

Stillwell J. — Yearning for the Impossible: The Surprising Truths of Mathematics

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: Yearning for the Impossible: The Surprising Truths of Mathematics

Автор: Stillwell J.

Аннотация:

This book explores the history of mathematics from the perspective of the creative tension between common sense and the "impossible" as the author follows the discovery or invention of new concepts that have marked mathematical progress:

* Irrational and Imaginary Numbers
* The Fourth Dimension
* Curved Space
* Infinity and others

The author puts these creations into a broader context involving related "impossibilities" from art, literature, philosophy, and physics. By imbedding mathematics into a broader cultural context and through his clever and enthusiastic explication of mathematical ideas the author broadens the horizon of students beyond the narrow confines of rote memorization and engages those who are curious about the place of mathematics in our intellectual landscape.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 250

Добавлена в каталог: 11.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Set of natural numbers      199
Set of points      197
set of rational numbers      197
Set of rational numbers has uncountably many gaps      202
Set of rational numbers has zero length      203
Set of rational numbers is countable      200
Set of real numbers is uncountable      202
Set, countable      197 200
Set, countable, does not fill line      202
Set, countable, has zero length      203
Set, uncountable      201 202
Set, uncountable, smallest      209
Shanks, William      84
Sine      42 190
Sine, hyperbolic      116
Sine, wave      190
Skolem, Thoralf      212
slope      52
Slope and area      93
Slope and parallels      54
Slope and tangents      89
Slope and the Pappus theorem      65
Slope of       91
Slope of $y = x^{n + 1}$       92
Slope of curves      90
Slope of parabola      89
Slope, limit of      90
Space has noncommuting rotations      142
Space, curved      108
Space, dodecahedral      189
Space, Euclidean      101 114 132
Space, finite      101
Space, flat      101 102 129
Space, hyperbolic      101 123 189
Space, infinite      102 198
Space, medieval      102
Space, non-Euclidean      116
Space, periodic      177 188
Space, rotation      141 142
Space, rotation, quaternion representation      143
Space, spherical      101
Space, topology of      195
Speiser, Andreas      107
Spherical geometry      112 114 116
Spherical geometry and Klein      125
Spherical geometry in non-Euclidean space      116
Spherical triangle      111
Spherical triangle, angle sum      112
Spivak, Michael      185
Square and the torus      187
Square, completing the      29
Square, origin of word      5
Square, root algorithm      15
Square, the circle      84 99 207
Stereographic projection      106
Stereographic projection, preserves circles      107
Stereographic projection, preserves infinitesimal shapes      107
Stevin, Simon      10
Stevin, Simon, and distributive law      27
Stevin, Simon, and equal temperament      21
Stevin, Simon, and irrationals      10 12
Stevin, Simon, De Thiende      15
Stevin, Simon, I'Arithmetique      10 27
Stevin, Simon, introduced infinite decimals      15
Stevin, Simon, Theory of the Art of Singing      22
String theory      213
Sum of complex numbers      34
Sum of infinitesimals      93
Sum of squares      140
Sum of two squares      164
Sum, infinite      83
Sum, limit of      100
Surd      xi
Surd, origin of word      9
Symmetry      144
Symmetry and motion      145
Symmetry and rotation      146
Symmetry of polyhedra      144
Symmetry, tetrahedral      146
Tangent      89
Tartaglia, Niccolo      30
Taylor, Brook      190
tetrahedron      81 144
Tetrahedron, rotations of      146 147
Tetrahedron, symmetry      146
Tetrahedron, symmetry, represented by quaternions      146 148
Tetrahedron, volume of      81
Theodoric      9
Theorem of Desargues      62 63

Theorem of Desargues and associative multiplication      75
Theorem of Desargues and Hubert      72 75
Theorem of Desargues as an axiom      65
Theorem of Desargues follows from Pappus      75
Theorem of Desargues, spatial version      63
Theorem of Pappus      62 63 76
Theorem of Pappus and commutative addition      73
Theorem of Pappus and commutative multiplication      74
Theorem of Pappus as an axiom      65
Theorem of Pappus, proof      64
Theorem, angle sum      110
Theorem, Bezout's      45
Theorem, factor      41
Theorem, Fermat's last      171
Theorem, Fundamental, of Algebra      41
Theorem, fundamental, of calculus      96
Theorem, little Desargues      66
Theorem, little Desargues, and Moufang      72
Theorem, Pascal's      62
Theorem, projective configuration      61
Theorem, Pythagorean      5 12 76
Three-square identity?      132
Tilings of $\mathbb{R}^3$       152
Tilings of $\mathbb{R}^4$       153
Tilings of $\mathbb{R}^n$       152 153
Tilings of hyperbolic plane      195
Tilings of the plane      152
Time      200
Time and infinitesimals      100
Tintoretto, Jacopo      107
topology      177
Topology and manifolds      189
Topology and periodicity      187
Topology of three-dimensional space      195
Topology, algebraic      195
Torricelli, Evangelista      156
Torus      see 2-torus 187
Tractrix      118
Transcendental, means nonalgebraic      205
Transcendental, number      xi
Triangle of negative curvature      119
Triangle, angle sum      50 112 116
Triangle, angle sum, detects curvature      111
Triangle, inequality      135
Triangle, spherical      111
Tribar      xi 177 179
Tribar in 3-cylinder      177 183
Trivium      2
Two-square identity      34 130
Two-square identity, complex      141
Ulam, Stan      198
Uncountability      201 202
Uncountability of $\mathbb{R}$       202
Uncountability, discovered by Cantor      202
Unique prime factorization      155
Unique prime factorization in Euclid      155
Unique prime factorization in positive integers      162
Unique prime factorization, assumed by Euler      170
Unique prime factorization, complex      155
Unique prime factorization, failure of      155 171
Unique prime factorization, Gaussian      163 168
Unique prime factorization, lost      169
Unique prime factorization, regained      172
UNITS      166 169
Van Ceulen, Ludolph      84
Vanishing points      55
Vector addition      131 136
Vector space      76
Vectors      131
Vermeer, Johannes      58
Vibration, frequency of      3
Vibration, modes of      3
Viete, Francois      36 38
Volume      11 79
Volume as sum of infinitesimals      93
Volume of box      80
Volume of parallelepiped      81
Volume of polyhedra      77
Volume of tetrahedron      81
Volume of triangular prism      81
Von Staudt, Christian      68 72
Von Staudt, Christian, and Pappus theorem      72
Wallis, John      98
Weber — Fechner law      4
Weeks, Jeffrey      189
Wessel, Caspar      38
Whole numbers      see numbers natural
Zhu Zaiyu      21
Zhu Zaiyu, computation of $\sqrt{2}$       22
Zu Chongzhi      84

1 2 3 4

О проекте