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Conics
The Mathematical Association of America | 2005-06-01 | ISBN: 0883853353 | 432 pages | Djvu | 9,7 MB
This book engages the reader in a journey of discovery through a spirited discussion among three characters: Philosopher, Teacher and Student. Throughout the book, Philosopher pursues his dream of a unified theory of conics, where exceptions are banished. With a helpful teacher and example-hungry student, the trio soon finds that conics reveal much of their beauty when viewed over the complex numbers. In their odyssey, they uncover a goldmine of unsuspected results.
They experience a series of 鈥淎ha!鈥?moments as they stumble upon living brothers to familiar conics objects like foci and directrices. They also discover a normally-unseen ellipse spanning the gap between the branches of any hyperbola. On the applied side, they learn how two interfering wave sources create systems of hyperbolas; these are used in making astonishingly precise astronomical observations. All these discoveries are profusely illustrated with pictures, worked-out examples, a generous selection of exercises, and a CD containing 36 applets. If you've ever needed a conics formula for area, eccentricity, curvature and the like, look in the formula appendix. Here are dozens of useful formulas-a set for each of eight different ways of looking at a conic: as a cone slice; as the path of a planet moving under the influence of a fixed sun; constructed using two stakes and string; plus five other sets. CONICS is written in an easy, conversational style, and many historical tidbits and other points of interest are scattered throughout the text. Many students can self-study the book without outside help. This book is ideal for anyone having a little exposure to linear algebra and complex numbers.
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