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Re: List of 'good' geometry textbooks
Posted:
Jul 22, 2001 9:11 PM
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I just wanted to day how saddened I am by the proposed constraints
within which a geometry book should be 'good'.
Formal proof IS a piece of mathematics - but only a piece.
To paraphrase my advisor (Gian Carlo Rota) formal proof is the
mathematics as medicine is to food.
I hate to see a classroom that tastes like a medicine cabinet rather
that the life of mathematics. It is particularly sad when a rich
and important subject like geometry is pushed into a box of
formal proof. Probably means very little transformations
(probably the key part of applications of geometry) and very
little 3-D geometry - at least until the students have been
so saturated in plane games that they have lost touch with
the world they live in.
Note that, since at least eh 1870's
the very DEFINITION of a geometry has revolved around transformations.
It is within that larger framework that many of the pieces in
Euclidean geometry take on a larger meaning in mathematics.
I recently saw a paper about testing students in grade 7, 9, 11
on some pencil and paper exercises about 3-D mirror symmetry.
(The kinds of things that are central to say, stereo chemistry.)
Students got WORSE in these exercises as they proceeded through school!
Sad indeed when we teach understanding out of students. There are many
geometry courses which accomplish that sad task.
Walter Whiteley
York University
Alan wrote:
>
> Thanks for all your input. Below is a list of geometry textbooks that
> have been recommended as 'good'. These recommendations were based on
> the book being targeted for high school honors/college level and one
> that rigorously covers Euclidian geometry with the major emphasis on
> formal proof. I am planning on reviewing all these books and will post
> my biased opinion rating each book.
>
> If you would like to add a book to the list, feel free!
>
> Thanks,
> Alan Sagan
>
> Here is the list:
> ---------------------------------
> Essentials of Geometry for College Students
> Arnold R. Steffensen, Northern Arizona University
> L. Murphy Johnson, Northern Arizona University
> Margaret L. Lial, American River College
> Publisher: Addison-Wesley
> Copyright: 1990
> Format: Cloth, 431 pp
> ISBN: 0-673-38419-5
> Addison-Wesley Pub Co; ISBN: 0201508672
> ---------------------------------
> Geometry
> by Moise, Downs
> Hardcover (January 1991)
> Addison-Wesley Pub Co; ISBN: 0201253356
> ---------------------------------
> Geometry for Enjoyment & Challenge
> Rhoad, Milauskas, Whipple
> Hardcover (June 1991)
> McDougal Littell & Co; ISBN: 0866099654
> ---------------------------------
> Geometry
> by Harold R. Jacobs (Editor)
> Hardcover - 668 pages 2nd edition (January 1987)
> W H Freeman & Co.; ISBN: 071671745X ; Dimensions (in inches): 1.28 x
> 10.23 x 7.86
> ---------------------------------
> College Geometry: A Problem Solving Approach with Applications, 1/e
> Gary L. Musser, Oregon State University
> Lynn Trimpe
> Copyright 1994, 528 pp.
> ISBN 0-02-385450-2
> ---------------------------------
> Geometry : Ancient and Modern
> by John R. Silvester
> Paperback (June 2001)
> Oxford Univ Press; ISBN: 0198508255
--
Walter Whiteley
Mathematics and Statistics
York University
whiteley@mathstat.yorku.ca
416-726-2100 ext 33971
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