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
... perceive the 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 ...
... perceive the 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 ...
Стр. 9
... perception and aesthetic appreciation, to the mathematical theory of symmetries, to the laws of physics, and to science in general, cannot be overemphasized, and I will return to it several times. Other symmetries do exist, however, and ...
... perception and aesthetic appreciation, to the mathematical theory of symmetries, to the laws of physics, and to science in general, cannot be overemphasized, and I will return to it several times. Other symmetries do exist, however, and ...
Стр. 11
... : In contrast to the impact of an artistic masterpiece, perceptual attention soon wanders, never goes deep. There is no enhancement of perception.” Actually, as I will show in the next chapter and in chapter 8, symmetry has. 11 SYMMETRY.
... : In contrast to the impact of an artistic masterpiece, perceptual attention soon wanders, never goes deep. There is no enhancement of perception.” Actually, as I will show in the next chapter and in chapter 8, symmetry has. 11 SYMMETRY.
Стр. 12
... perception. For the moment, however, let me concentrate on the purely aesthetic “value” of symmetry. Dartmouth College psychologists Peter G. Szilagyi and John C. Baird conducted a fascinating experiment in 1977 that was intended to ...
... perception. For the moment, however, let me concentrate on the purely aesthetic “value” of symmetry. Dartmouth College psychologists Peter G. Szilagyi and John C. Baird conducted a fascinating experiment in 1977 that was intended to ...
Стр. 13
... perception; (2) the realization that the object is distinguished by a certain order; (3) the appreciation of value that rewards the mental effort. Birkhoff further assigns quantitative measures to the three stages. The preliminary ...
... perception; (2) the realization that the object is distinguished by a certain order; (3) the appreciation of value that rewards the mental effort. Birkhoff further assigns quantitative measures to the three stages. The preliminary ...
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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