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The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Lan |  |
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The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Lan | |
For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two great prodigies ultimately proved that the quintic cannot 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 beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history.
作者简介 Mario Livio is a senior astrophysicist and the Head of the Office of Public Outreach at the Space Telescope Science Institute (STScI) in Baltimore, Maryland. He is the author of The Golden Ratio, a highly acclaimed book about mathematics and art for which he received the International Pythagoras Prize and the Peano Prize, The Equation That Couldn't Be Solved, and The Accelerating Universe. He lives in Baltimore, Maryland.
编辑推荐 A wide-ranging exploration of the phenomenon of symmetry....There's math, yes, but there are also tales of love, violence, history -- and the whole, in this case, turns out to be greater than the sum of those parts.-- Mary Carmichael, Newsweek^"Fascinating. . . . [Livio] writes passionately about the role of symmetry in human perception and the arts."-- The Economist^"A lively and fascinating read for a broad audience."-- Nature
目录
Contents
Preface
1. Symmetry
2. eyE s'dniM eht ni yrtemmyS
3. Never Forget This in the Midst of Your Equations
4. The Poverty-Stricken Mathematician
5. The Romantic Mathematician
6. Groups
7. Symmetry Rules
8. Who's the Most Symmetrical of Them All?
9. Requiem for a Romantic Genius
Appendix 1. Card PuzzleAppendix 2. Solving a System of Two Linear Equations
Appendix 3. Diophantus's Solution
Appendix 4. A Diophantine Equation
Appendix 5. Tartaglia's Verses and Formula
Appendix 6. Adriaan van Roomen's Challenge
Appendix 7. Properties of the Roots of Quadratic Equations
Appendix 8. The Galois Family Tree
Appendix 9. The 14-15 Puzzle
Appendix 10. Solution to the Matches Problem
Notes
References
Index
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文摘 Chapter One: Symmetry
An inkblot on a piece of paper is not particularly attractive to the eye, but if you fold the paper before the ink dries, you may get something that looks like figure 1 that is much more intriguing. In fact, the interpretation of similar inkblots forms the basis for the famous Rorschach test developed in the 1920s by the Swiss psychiatrist Hermann Rorschach. The declared purpose of the test is to somehow elicit the hidden fears, wild fantasies, and deeper thoughts of the viewers interpreting the ambiguous shapes. The actual value of the test as an "x-ray of the mind" is vehemently debated in psychological circles. As Emory University psychologist Scott Lilienfeld once put it, "Whose mind, that of the client or the examiner?" Nevertheless, there is no denial of the fact that images such as that in figure 1 convey some sort of attractive and fascinating impression. Why?
Is it because the human body, most animals, and so many human artifacts possess a similar bilateral symmetry? And why do all those zoological features and creations of the human imagination exhibit such a symmetry in the first place?
Most people perceive harmonious compositions such as Botticelli's Birth of Venus as symmetrical. Art historian Ernst H. Gombrich even notes that the "liberties which Botticelli took with nature in order to achieve a graceful outline add to the beauty and harmony of the design." Yet mathematicians will tell you that the arrangements of colors and forms in that painting are not symmetric at all in the mathematical sense. Conversely, most nonmathematical viewers do not 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 aesthetic sensibility? In the scientific realm, why has symmetry become such a pivotal concept in our ideas about the c
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