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.
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Try http://matheducators.stackexchange.com. – lhf Aug 19 '15 at 12:01
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I don't know have any textbooks to recommend, but I was curious whether something interesting would turn up if I poked around what's used in some high school honors geometry courses (unfortunately, in the past 20 or 25 years I think "honors" has come to mean little more than what "college prep" meant 40 years ago), and I found this interesting page of parent comments. Anyway, for starters try googling "honors geometry" along with "high school". – Dave L. Renfro Aug 19 '15 at 18:58
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I recently read somewhere (forgot where, but it wasn't on the internet) about the existence of a high school geometry book co-authored by George David Birkhoff. I haven't seen a copy of the book yet, but any serious attempt by someone as renowned as G. D. Birkhoff is very definitely worth looking into. See Basic Geometry (3rd edition) and Basic Geometry - Manual for Teachers, both by George David Birkhoff and Ralph Beatley. – Dave L. Renfro Oct 07 '15 at 17:24
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I'd recommend advanced high-school mathematics by David B. Surowski. – athos Aug 30 '22 at 21:05
2 Answers
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.
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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").
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