Special Properties of Conics

This issue's Geometer's Corner is written by two students, Cynthia Liu and Soonkyu Park, who are taking a tutorial with me this year. We have been taking an intensive look at the conics and making extensive use of Cabri 3D and GeoGebra in our work. For the past month, we have been studying a new book that the American Mathematical Society is publishing: Geometry of Conics by A.V. Akopyan and A.A. Zaslavsky.

What Cynthia and Soonkyu have written will give you a feel for the book. It is an ideal book for a senior level high school elective for students who have studied the conics and would like to study more geometry. It is also a great book for teachers to learn more about the conics and, in the process, learn some useful mathematical techniques, such as inversion.

All the figures in the article were made with GeoGebra, a free computer based geometric construction package that has many useful features lacking in Cabri 2 and the Geometer's SketchPad. I have the actual GeoGebra files that were used on myWebsite, www.zebragraph.com. Please feel free to download them.