Subject: Re: [HM] reference request -- Klein
From: David Stump (stumpd@usfca.edu)
Date: Thu Jan 06 2000 - 12:17:37 EST
I cannot say I have solved the original mystery that prompted the query,
but I did receive some very nice references for which I am very grateful
and that I will share with the list.
--------------
Volume 10 in the series HISTORY OF MATHEMATICS, published jointly by the
AMS and the LMS, seems relevant. It is titled "Sources of Hyperbolic
Geometry" and contains a number of translations. The translator, John
Stillwell, wrote enlightening introductions to the papers in this
collection. One of these papers is Klein's "On the so-called Non-Euclidean
Geometry".
Here are two items of obvious "Klein relevance":
1. Klein's famous programmatic lecture Vergleichende Betrachtungen ueber
neue geometrische Forschungen, Erlangen, 1872.
2. Ch. 12 in vol.II of the three-volume "Fundamentals of Mathematics",
published by MIT in 1974. (This is a translation from the German by
S.H. Gould. It is annoying that a man of Gould's erudition should use
the term ERLANGER PROGRAM, which is half German and half English.)
Anyone interested in seeing Klein's geometries in action should read
I.M. Yaglom's "A simple Non-Euclidean Geometry and Its Physical Basis",
which I translated for Springer in 1979.
Best wishes,
Abe Shenitzer
--------------
I do not remember the book you are looking for, but I can offer you a
few titles of books in German on non-euclidean geometry. With some luck,
the book you want may be found, starting from the following short list:
H. Meschkowski: Nichteuklidische Geometrie. (3. Aufl.: Braunschweig 1965.)
O Perron: Nichteuklidische Elementargeometrie der Ebene. Stuttgart 1962
L. Heffter: Grundlagen und analytischer Aufbau der projektiven,
euklidischen, nichteuklidischen Geometrie. (3. Aufl.: Stuttgart 1958).
Yours, Peter Flor.
--------------
At 11:55 AM 12/31/99 -0800, David Stump wrote:
>
> I thought I had a reference to a book, in German, that discusses Felix
> Klein's work on non-Euclidean geometry and sorts out the sequence of
> various editions, etc. I think this book may have even been mentioned
> on this list, but now I cannot find it. Is this perhaps my long awaited
> Y2K problem, or was I imagining the book? Please let me know if anyone
> remembers something along these lines. I am especially interested in
> Klein's presentation of his model to show the relative consistency of
> BL. Works in English or French would also be welcome. Please send me
> messages directly and I will post a summary to the list.
>
> Thank you and happy new year.
David J. Stump voice: (415) 422-6153
Department of Philosophy FAX: (415) 422-5356
University of San Francisco email: stumpd@usfca.edu
2130 Fulton Street
San Francisco, CA 94117-1080 USA
This archive was generated by hypermail 2b28 : Thu Jan 06 2000 - 13:08:50 EST