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Re: List of 'good' geometry textbooks
Posted:
Jul 22, 2001 9:11 PM


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 3D 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 3D 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: AddisonWesley > Copyright: 1990 > Format: Cloth, 431 pp > ISBN: 0673384195 > AddisonWesley Pub Co; ISBN: 0201508672 >  > Geometry > by Moise, Downs > Hardcover (January 1991) > AddisonWesley 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 0023854502 >  > 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 4167262100 ext 33971



