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To the pure geometer the radius of curvature is an incidental characteristic - like the grin of the Cheshire cat. To the physicist it is an indispensable characteristic. It would be going too far to say that to the physicist the cat is merely incidental to the grin. Physics is concerned with interrelatedness such as the interrelatedness of cats and grins. In this case the "cat without a grin" and the "grin without a cat" are equally set aside as purely mathematical phantasies.
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Historical Topics for the Mathematics Classroom
Historical Topics for the Mathematics Classroom, J.K. Baumgart, D.E. Deal, B.R. Vogeli, A.E. Hallerberg, eds., NCTM 1989. 542 pages, $37.95, softcover, ISBN 0-87353-281-3. Revision of 1969 edition. The National Council of Teachers of Mathematics, Inc. 1906 Association Drive, Reston, Virginia, 20191. (800) 235-7566. www.nctm.org
This book is a wonderful resource for teachers of Mathematics. It is an easily read and absorbing overview of the history of mathematics with suggestions for its use in the classroom. The history of each major branch of mathematics (Number, Computation, Algebra, Geometry, Trigonometry and Calculus) is individually summarized and followed by brief essays on specific topics of significance within each branch. This organization makes it easy to find and quickly read the informative articles on any chosen topic. The writing style and reading levels of most articles also make them available to high school students.
The last two chapters of the book present an overview of the development of modern mathematics originating in the nineteenth century and a perspective on contemporary mathematics as a science of patterns. These chapters give a brief, integrated view of the direction of mathematics development over the last century. Again, the treatment is very easy to read and very informative for teachers and more advanced students. Finally an Appendix that discusses other resources and two bibliographies (original and updated) aid the teacher to include historical topics in teaching mathematics
While originally published in 1969, and updated in 1989, this most recent printing continues to offer high school and university teachers an excellent tool for the classroom and their own development. Hopefully, a new edition will soon be published with updates to the chapters on modern mathematics and the Appendix and Bibliographies to include some of the excellent work published over the last fifteen years.
Tim Keenan, Mathematics Teacher, Osbourn Park High School, Prince William County, Virginia