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

J. W. Downs
Dover Publications
Publication Date: 
Number of Pages: 
[Reviewed by
Underwood Dudley
, on

The subtitle of this 100-page paperbound book, priced at $11.95, is “the geometric properties of ellipses, parabolas, and hyperbolas.” The author’s objective is “to give a conceptual understanding of conic curves — something that is almost totally lost when these curves are reduced to mathematical formulas.”

The book is called practical because the author has “tried to avoid the tedious proofs that abound in most books on the subject.” Its content is almost exclusively geometrical and includes many methods for constructing conic sections and considers some of their properties, including reflection properties that have applications to telescopes, antennas, and sound systems. The writing is clear and good, as are the diagrams.

The book was originally published by Dale Seymour Publications with the comment “Reading level — ages 9 and up.” One of the reviewers of the book on was a student who had to write a paper on the conic sections and said that the book made his time in the library “short and sweet.” Students are probably the best audience for the book. Its age is shown by the 6% of its pages given over to a BASIC program for finding points on conics.

Woody Dudley stopped teaching about conics and everything else in 2004. He still likes books.

1. Deriving Ellipses.
2. Deriving Hyperbolas.
3. Deriving Parabolas.
4. The Directing Circle.
5. Reflective Properties of Solid Conic Curves.
6. Compound Reflectors.
7. Eccentricity.
8. For Practical Purposes.
9. Unusual Properties of Cones and Conic Curves.
Appendices. Bibliography.