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John,
As far as I know, Adams's monograph is the first and last use of
Abelian integrals in a cartographic context. If there have been other
studies of them pertaining to maps, those studies were published well
outside the usual venues. I have to think that happens in the
mathematics literature, since mathematicians refer to a much broader
range of things as "mappings". If someone slipped some cartographic
application into their work, it could get overlooked, disguised by
"mappings" in general.
Regards,
— daan Strebe
On May 11, 2010, at 6:57 AM, John W. Hessler wrote:
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Histers,
A question for all you projection fans....????
I am currently finishing up a very long article for the 20th
Century volume of the "History of Cartography" called "Mathematics
and Cartography". The article highlights the entrance into
cartography of results and theorems from pure mathematics like
existence theorems, modular form, fractals, differential topology
etc, etc....
I am having trouble verifying the appearance in cartographic
literature of Abelian Integrals. C.S. Pierce published an account of
a conformal projection of a sphere in a square in 1889 and this
followed the work of E. Guyou who solved a related projection in
1887. Both of these are based on the use of Elliptic Integrals. In
1925 Oscar Adams of the Coast and Geodetic Survey published a small
booklet called 'Elliptic Functions Applied to Conformal Maps' where
he extends this theory of elliptic integrals using Abelian functions
developed in series solutions. This is an important historical
development because it represents some of the most interesting
applications of the theory of functions of a complex variable in
cartography. Is this the first and nearly last use of Abelian
functions for cartographic purposes...????
Thanks..
John W. Hessler
Fellow of the Royal Geographical Society
Senior Cartographic Librarian
Geography and Map Division
Library of Congress
Washington DC
202-707-7223
Website:
http://www.warpinghistory.blogspot.com
What any picture, of whatever form, must have in common
with reality in order to depict it--correctly or incorrectly--
in any way at all, is logical form, i.e. the form of reality.
--Wittgenstein
Tractatus Logico-Philosophicus
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Utrecht. The University of Utrecht does not take any responsibility for
the views of the author.
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