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mathwonk
Posts:
4
From:
georgia
Registered:
5/21/07
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Re: hs geometry text
Posted:
May 21, 2007 7:14 PM
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Im having the same problem. One reason is the subject is very subtle. For example the SAS "theorem" was not proved correctly in Euclid, and thus it is necessary to make it either a postulate or introduce some other device which allows it to be correctly proved.
On the other hand conceopts like between are so hard to get right that when I have done so in a course it has killed off the students through excessive focus on fine points.
I myslef liked Harold Jacobs Geometry but not the third edition, which seems mickey mouse compared to the earlier two. but it does not discuss the very subtle plane separation postulates euclid omitted. (i.e. it assumes thigns like the fact that a line meeting a triangle away from a vertex, must meet it again somewhere, or that a circle meeting another circle at a point not collinear with their centers meets it a second time. actually euclid discussed some of these things but in a somewhat unclear way, to me.)
if you want a super rigorous book for a brilliant kid, the book by millman and parker is as rigorous as could be desired, but uses some calculus in one place, unless you want to take trig functions for granted like sine and cosine.
you might enjoy combining a copy of euclid himself such as a free version online, with a book discussing its flaws, like hartshorne's geometry: euclid and beyond.
or an old copy of the yale universty press books from the 1960's on geometry, part of the old SMSG program. if you can find them, maybe in a math ed department library.
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