Re: Help: A suitable set of postulates for High School Geometry
- From: "Karl M. Bunday" <kmbunday@xxxxxxxxxxxx>
- Date: Sat, 09 Jul 2005 23:21:57 GMT
Ronald wrote, in reply to an earlier reply in this thread:
Not hardly. Euclid's axioms have too many holes and implicit assumptions.
I suppose the simplest set is Hilbert's. Not too appropriate for high-school, perhaps.
The Education Program for Gifted Youth (EPGY) geometry course
http://epgy.stanford.edu/courses/math/M015/
essentially implements Hilbert's axioms, and has a good discussion of what axioms are necessary for "Euclidean" plane geometry. I know several young people who have used that course as distance learning students. They are "gifted" students, and I don't suppose average high school students would necessarily fare well with the same approach.
Another participant mentioned the school mathematics study group postulates, as one mentioned Birkhoff's postulates. Some melange of those quite similar sets of postulates is the basis for most high school geometry instruction today that so much as mentions axiom systems. If you see a "ruler postulate" relating real numbers to points on the number line, you know you are seeing that kind of approach.
Judith Cederberg's book A Course in Modern Geometries (Springer-Verlag)
http://www.amazon.com/exec/obidos/tg/detail/-/0387989722/
contains a discussion of varying axiom systems for high school geometry, listing the axioms of the major systems.
-- Karl M. Bunday P.O. Box 1456, Minnetonka MN 55345 Learn in Freedom (TM) http://learninfreedom.org/ remove ".de" to email .
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