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Topic: Any updated books as good as Euclids elements?
Replies: 3   Last Post: Feb 11, 2008 7:25 AM

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Walter Whiteley

Posts: 418
Registered: 12/3/04
Re: Any updated books as good as Euclids elements?
Posted: Feb 11, 2008 7:25 AM
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However, Hilbert's very interesting exploration was more for the
benefit of logicians and the foundations of eulcidean geometry. It
is not usable for teaching new-comers, or for assisting or describing
how people now doing/ using geometry practice geometric reasoning.

To paraphrase my advisor (Gian-Carlo Rota)
'this axiomatic presentation of geometry is to the practice of
geometry as medicine is to food'.
The axioms point out some areas of concern that should be raised to
our attention under certain circumstances, but do not serve the
teaching and learning of geometry most of the time.

In my practice of discrete applied geometry, and in my teaching /
research on mathematics education, Felix Klein has been a
substantially larger influence with his Erlanger Program. It is no
accident that one of the two most prestigious prizes in Mathematics
Education is named after Klein. The other is named after Hans
Freudenthal, who has also written about geometry. There is a nice
article by Freudenthal, in JSTOR: Geometry between the devil and the
deep sea. I note that to Freudenthal, 'the devil' was the axiomatic
approach to geometry! He preferred to be in the deep sea.

Walter Whiteley
York University

On 10-Feb-08, at 8:44 PM, Kirby Urner wrote:

"David Hilbert was one of the outstanding mathematicians of the
modern era. He proposed 21 geometry axioms--the greatest influence in
geometry since Euclid (325 BC)."


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