Introduction to NON-EUCLIDEAN GEOMETRY by HAROLD E. WOLFE . PREFACE
This book has been written in an attempt to provide a satisfactory
textbook to be used as a basis for elementary courses in Non-Euclid
ean Geometry. The need for such a volume, definitely intended for
classroom use and containing substantial lists of exercises, has
been evident for some time. It is hoped that this one will meet the
re quirements of those instructors who have been teaching the
subject tegularly, and also that its appearance will encourage
others to institute such courses. x The benefits and amenities of a
formal study of Non-Euclidean Geometry are generally recognized.
Not only is the subject matter itself valuable and intensely
fascinating, well worth the time of any student of mathematics, but
there is probably no elementary course which exhibits so clearly
the nature and significance of geometry and, indeed, of mathematics
in general. However, a mere cursory acquaintance with the subject
will not do. One must follow its development at least a little way
to see how things come out, and try his hand at demonstrating
propositions under circumstances such that intuition no longer
serves as a guide. For teachers and prospective teachers of
geometry in the secondary schools the study of Non-Euclidean
Geometry is invaluable. With out it there is strong likelihood that
they will not understand the real nature of the subject they are
teaching and the import of its applications to the interpretation
of physical space. Among the first books on Non-Euclidean Geometry
to appear in English was one, scarcely more than a pamphlet,
written in 1880 by G. Chrystal. Even at that early date the value
of this study forthose preparing to teach was recognized. In the
preface to this little brochure, Chrystal expressed his desire to
bring pangeometrical speculations under the notice of those engaged
in the teaching of geometry He wrote It will not be supposed that I
advocate the introduction of pan geometry as a school subject it is
for the teacher that I advocate vi PREFACE such a study. It is a
great mistake to suppose that it is sufficient for the teacher of
an elementary subject to be just ahead of his pupils. No one can be
a good elementary teacher who cannot handle his subject with the
grasp of a master. Geometrical insight and wealth of geometrical
ideas, either natural or acquired, are essential to a good teacher
of geometry and I know of no better way of cultivat ing them than
by studying pan geometry. Within recent years the number of
American colleges and uni versities which offer courses in advanced
Euclidean Geometry has increased rapidly. There is evidence that
the quality of the teaching of geometry in our secondary schools
has, accordingly, greatly improved. But advanced study in Euclidean
Geometry is not the only requisite for the good teaching of Euclid.
The study of Non-Euclidean Geometry takes its place beside it as an
indispensable part of the training of a well-prepared teacher of
high school geometry. This book has been prepared primarily for
students who have completed a course in calculus. However, although
some mathe matical maturity will be found helpful, much of it can
be read profitably and with understanding by one who has completed
a secondary school course in Euclidean Geometry. He need only omit
Chapters V and VI, which make use of trigonometry and calcu lus,
and thelatter part of Chapter VII. In Chapters II and III, the
historical background of the subject has been treated quite fully.
It has been said that no subject, when separated from its history,
loses more than mathematics. This is particularly true of
Non-Euclidean Geometry...
General
| Imprint: |
Read Books
|
| Country of origin: |
United Kingdom |
| Release date: |
March 2007 |
| First published: |
March 2007 |
| Authors: |
Harold E. Wolfe
|
| Dimensions: |
216 x 140 x 14mm (L x W x T) |
| Format: |
Paperback - Trade
|
| Pages: |
260 |
| ISBN-13: |
978-1-4067-1852-2 |
| Categories: |
Books >
Science & Mathematics >
Science: general issues >
General
|
| LSN: |
1-4067-1852-1 |
| Barcode: |
9781406718522 |
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