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Full Description
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. It is profusely illustrated with pictures, worked-out examples, and a CD containing 36 applets. 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.
Contents
1. Beauty and the beast; 2. Life at infinity; 3. How to gift-wrap a hyperbola; 4. The cube; 5. The other foci: a well kept secret; 6. Are hyperbolas really ellipses?; 7. Stakes and strings; 8. Directrices, new and old; 9. Conics in general position; 10. A beautiful mathematical universe; 11. A most excellent theorem; 12. The big view; 13. Curvature; 14. Curvature of conics; 15. Photons and conics; 16. How conics solved a 2000-year-old question; 17. Waves and conics; Appendix 1 some conics formulas; Appendix 2 Topology: a quick handshake.