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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... instance, would be kept warm in the cold Chicago winters. Clearly, other shortcomings would be associated with such a configuration. The hearing of armpit ears would be seriously impaired unless you kept your arms raised all the time ...
... instance, would be kept warm in the cold Chicago winters. Clearly, other shortcomings would be associated with such a configuration. The hearing of armpit ears would be seriously impaired unless you kept your arms raised all the time ...
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... instance, 65 percent of the subjects created perfect mirror-reflectionsymmetric 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 ...
... instance, 65 percent of the subjects created perfect mirror-reflectionsymmetric 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 ...
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... instance, the equilateral (all sides the same) triangle in figure 9a. We are allowed neither to change the shape or size of this triangle, nor to move it about. What Figure 8 a b the visual field. Figure 25 Figure 26 affected, for ...
... instance, the equilateral (all sides the same) triangle in figure 9a. We are allowed neither to change the shape or size of this triangle, nor to move it about. What Figure 8 a b the visual field. Figure 25 Figure 26 affected, for ...
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... instance, can be expressed as ABACA or ABACABA, where the translational symmetry is apparent. Mozart's association with objects of mathematics should come as no surprise. His sister, Nannerl, recalled that he once covered the walls of ...
... instance, can be expressed as ABACA or ABACABA, where the translational symmetry is apparent. Mozart's association with objects of mathematics should come as no surprise. His sister, Nannerl, recalled that he once covered the walls of ...
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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 | |
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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 |
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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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