Conics

The Dolcoiani Mathematical Expositions #29

Keith Kendig

432 pages, parution le 07/12/2005

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Résumé

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 "Aha!" 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, 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.

System Requirements for running the applets

Windows

Pentium 4: Windows NT/2000, or Windows XP
128MB of RAM
Internet Explorer 6 SP1 or later.
Java: Java Plug-in TM version 1.42 or later. A free update is available at http://www.java.com.

Macintosh

G4 or G5 processor: Mac OS X v. 10.3.4 or later
Safari browser recommended for the Mac
128MB of RAM
Java: Java Plug-in TM version 1.42 or later. A free update is available at http://www.java.com.

Sommaire

Beauty and the Beast
Life at Infinity
How to Gift-Wrap a Hyperbola
The Cube
The Other Foci: a Well-Kept Secret
Are Hyperbolas Really Ellipses?
Stakes and Strings
Directrices, New and Old
Conics in General Position
A Beautiful Mathematical Universe
A Most Excellent Theorem
The Big View
Curvature
Curvature of Conics
Photons and Conics
How Conics Solved a 2000-Year-Old Problem
Waves and Conics
Appendix 1 Some Conics Formulas
Appendix 2 Topology: A Quick Handshake

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Caractéristiques techniques

	PAPIER
Éditeur(s)	The Mathematical Association of America (MAA)
Auteur(s)	Keith Kendig
Parution	07/12/2005
Nb. de pages	432
Format	18,5 x 26,5
Couverture	Relié
Poids	910g
Intérieur	Noir et Blanc
EAN13	9780883853351
ISBN13	978-0-88385-335-1