High School Geometry Text?

Question

This year I will be teaching 8 hard-working home-educated teens a Geometry course. Back in 1994-1999 I worked full time as a High School educator, taking a turn teaching everything from Pre Algebra through Basic Calculus, and Geometry was (and still is) my favorite. I am wanting to buy (at abebooks or some such place) a stack of student books and a teacher's edition. Recommendations? In some ways the recent editions may be better. In other ways . . . not so much. I recall being aghast as a teacher at how "dumbed down" the texts had become just in the few years between my being a high school student and a high school teacher. And that was 20 years ago. If you have a specific publisher and year (Prentice Hall 1989, as a random example) that you enjoyed using as a teacher, I'd love to hear your comments.

Answer 1

How about Lines and Curves by Gutenmacher and Vasilyev (Springer, 2013); about this book:

"Lines and Curves" is a unique adventure in the world of geometry. Originally written in Russian and used in the Gelfand Correspondence School, this work has since become a classic: unlike standard textbooks that use the subject primarily to introduce axiomatic reasoning through formal geometric proofs, "Lines and Curves" maintains mathematical rigor, but also strikes a balance between creative storytelling and surprising examples of geometric properties.

I didn't finish reading the book, but as to the parts I have read, I can attest to the summary. Here is the book at AbeBooks.

Answer 2

If you don't have any particular curriculum to follow, the best textbooks in English are probably the ones commonly used in England during the period 1910-1960 approximately.

The most frequently recommended school books in bibliographies seem to be those by C.V. Durell and by H.G. Forder.

• A number of Durell's textbooks can be found here. A New Geometry for Schools is for beginners. Modern Geometry is more advanced.

• Forder wrote A School Geometry and Higher Course Geometry. I only know the latter book, which is more advanced, but I believe they're both aimed at high-achieving students.

Kiselev's Geometry was recently translated from Russian under the titles Planimetry and Stereometry. I think the textbook is relatively good, but unfortunately, the translation is poor, as it was done by a non-native speaker of English.

In French, I would recommend the series by Hémery and Lebossé. In Russian, the books by Pogorelov are good, as well as the ones by Aleksandrov, Verner and Ryzhik (for students in so-called "mathematical schools").