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Re: List of 'good' geometry textbooks
Posted:
Jul 22, 2001 9:48 PM
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Thank you for your comments. I hope others read them and think about them.
They are right on target.
John Threlkeld
Graland Country Day School
Denver, CO
----- Original Message -----
From: "Walter Whiteley" <whiteley@mathstat.yorku.ca>
To: "Alan" <alansagan@hotmail.com>
Cc: <geometry-pre-college@forum.mathforum.com>
Sent: Sunday, July 22, 2001 7:11 PM
Subject: Re: List of 'good' geometry textbooks
> 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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