Practical Conic Sections The Geometric Properties of Ellipses, Parabolas and Hyperbolas,9780486428765

Practical Conic Sections The Geometric Properties of Ellipses, Parabolas and Hyperbolas

by
ISBN13: 9780486428765
ISBN10: 0486428761
Format: Paperback
Pub. Date: 2010-10-18
Publisher(s): Dover Publications
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Summary

Illustrated with interesting examples from everyday life, this text shows how to create ellipses, parabolas, and hyperbolas. It also presents historical background on their ancient origins and describes the reflective properties and roles of curves in design applications. Only a basic knowledge of plane geometry needed. 1993 edition. Includes 98 figures.

Table of Contents

Preface vi
Introduction vii
Deriving Ellipses
1(9)
Deriving Hyperbolas
10(7)
Deriving Parabolas
17(8)
The Directing Circle
25(11)
Constructing an Ellipse
26(2)
Constructing a Hyperbola
28(2)
Constructing a Parabola
30(1)
Points of Tangency
31(3)
Comparing Conic Curves
34(2)
Reflective Properties of Solid Conic Curves
36(10)
Ellipsoids
36(5)
Hyperboloids
41(2)
Paraboloids
43(3)
Compound Reflectors
46(9)
Cassegrain Systems
46(2)
Gregorian Systems
48(1)
Using the Cassegrain Principle
48(2)
Compound Reflector Design
50(5)
Eccentricity
55(5)
Special Cases
56(4)
For Practical Purposes
60(8)
Telescopes
60(1)
Sound Applications
60(2)
Variations
62(3)
Acoustical Applications
65(3)
Unusual Properties of Cones and Conic Curves
68(22)
An Interesting Proof
68(3)
Cones
71(3)
Ellipses
74(1)
Kepler's Laws
75(7)
Orbital Velocities
82(1)
Elliptical Gears
83(1)
Sketching Conics from a Formula
84(5)
Conclusion
89(1)
Appendix A Nonparabolic Reflectors for Antennas 90(5)
Appendix B Computer Program for Generating Conic Curves 95

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