The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of SymmetrySimon and Schuster, 19 сент. 2005 г. - Всего страниц: 368 The author of The Golden Ratio tells the “lively and fascinating” story of two nineteenth-century mathematicians whose work revealed the laws of symmetry (Nature). What do Bach’s compositions, Rubik’s Cube, the way we choose our mates, and the physics of subatomic particles have in common? All are governed by the laws of symmetry, which elegantly unify scientific and artistic principles. Yet the mathematical language of symmetry—known as group theory—did not emerge from the study of symmetry at all, but from an equation that couldn’t be solved. For three centuries, the quintic equation resisted efforts by mathematicians to find a solution. Working independently, two great prodigies ultimately proved that it couldn’t be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn’t Be Solved is told not through abstract formulas but in a dramatic account of the lives and work of some of the greatest mathematicians in history. |
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Стр. 2
... pattern in figure 3 as symmetrical, even though it actually is symmetrical according to the formal mathematical definition. So what is symmetry really? What role, if any, does it play in perception? How is it related to our aesthetic ...
... pattern in figure 3 as symmetrical, even though it actually is symmetrical according to the formal mathematical definition. So what is symmetry really? What role, if any, does it play in perception? How is it related to our aesthetic ...
Стр. 11
... pattern that provokes such an emotional response? And is this truly the same excitement that is stimulated by works of ... patterns may not be too different (even if less intense perhaps) from our broader aesthetic sensibility. Not all ...
... pattern that provokes such an emotional response? And is this truly the same excitement that is stimulated by works of ... patterns may not be too different (even if less intense perhaps) from our broader aesthetic sensibility. Not all ...
Стр. 12
... patterns in the first task. In fact, symmetry was the primary component in the designs of most subjects (in one, two, and three dimensions), with perfect symmetry being the most favored condition. The association between symmetry and ...
... patterns in the first task. In fact, symmetry was the primary component in the designs of most subjects (in one, two, and three dimensions), with perfect symmetry being the most favored condition. The association between symmetry and ...
Стр. 15
... patterns is that of a repeating, recurring motif. From friezes of classical temples and pillars of palaces to carpets and even birdsong, the symmetry of repeating patterns has always produced a very comforting familiarity and a ...
... patterns is that of a repeating, recurring motif. From friezes of classical temples and pillars of palaces to carpets and even birdsong, the symmetry of repeating patterns has always produced a very comforting familiarity and a ...
Стр. 16
... pattern is called symmetric if it can be displaced in various directions without looking any different. In other words, regular designs in which the same theme repeats itself at fixed intervals possess translational symmetry. Ornaments ...
... pattern is called symmetric if it can be displaced in various directions without looking any different. In other words, regular designs in which the same theme repeats itself at fixed intervals possess translational symmetry. Ornaments ...
Содержание
1 | |
2 eyE sdniM eht ni yrtemmyS | 29 |
3 Never Forget This in the Midst of Your Equations | 51 |
4 The PovertyStricken Mathematician | 90 |
5 The Romantic Mathematician | 112 |
6 Groups | 158 |
7 Symmetry Rules | 198 |
8 Whos the Most Symmetrical of Them All? | 233 |
Appendix 4 A Diophantine Equation | 281 |
Appendix 5 Tartaglias Verses and Formula | 282 |
Appendix 6 Adriaan van Roomens Challenge | 285 |
Appendix 7 Properties of the Roots of Quadratic Equations | 286 |
Appendix 8 The Galois Family Tree | 288 |
Appendix 9 The 1415 Puzzle | 291 |
Appendix 10 Solution to the Matches Problem | 292 |
Notes | 293 |
9 Requiem for a Romantic Genius | 262 |
Appendix 1 Card Puzzle | 277 |
Appendix 2 Solving a System of Two Linear Equations | 278 |
Appendix 3 Diophantuss Solution | 280 |
309 | |
337 | |
Другие издания - Просмотреть все
The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the ... Mario Livio Ограниченный просмотр - 2005 |
The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the ... Mario Livio Недоступно для просмотра - 2006 |
The Equation that Couldn't be Solved: How Mathematical Genius Discovered the ... Mario Livio Недоступно для просмотра - 2005 |
Часто встречающиеся слова и выражения
Abel Abel’s algebra appeared bilateral symmetry brain Cardano Cauchy century chapter creative Crelly cube cubic degrees Demante denoted described discovered Earth’s École Einstein electrons entire Évariste Galois Évariste’s examination fact famous father Ferrari Ferro figure followed force formula French Galois group Galois’s genius geometry gravity group of permutations group theory Guigniault human ideas identity instance inverse Klein known later laws of nature letter Lie groups mathe mathematician mathematics memoir metry O’Connor and Robertson objects operation paper Paris particles patterns perception physicists physics precisely problem proof properties proton psychologist published puzzle quadratic equations quantum mechanics quarks quintic equation reflection relativity result rotation Ruffini Scipione dal Ferro showed simple groups solution solvable solve spacetime special relativity speed of light spin Stéphanie’s string theory subgroup supersymmetry symmetry transformations Tartaglia theorem tion translation University whole number Woerden words young
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