Subject: [HM] rediscovered quartics
From: Jonathan Chertok (chertok22@hotmail.com)
Date: Wed Feb 09 2000 - 10:48:12 EST
Note: Non-member submission
Comment: Approved by Service Moderator #2
Dear List,
I am looking to model some quartic surfaces first generated by a professor
Sucharda in the 1880's. One of these is the Bohemian Dome and all are
generated by rotating conic sections about conic sections. I have found the
Bohemian Dome, but do not see the others modelled or in any published
literature.
Here is my progress to date:>
1. I have located an article by Sucharda in Czech and am told by a
mathematician that in order to get the mechanical (i.e. verbal)description
of these quartics (for the bohemian dome it starts "rotate a circle about
another circle...") that I would need a mathematician to be able to
visualize the mathematical descriptions in this article who would then
translate this to a verbal/mechanical description.
2. There is a site called the Jahrbuch Database which lists all of
Sucharda's publications and I am currently waiting for a German friend to
see if any of these other articles might have the verbal/mechanical
description already in written form. It is:
http://www.emis.de/MATH/JFM/JFM.html
You can see these articles by going to the web page and simply typing in
Sucharda as author to do the search. I believe there are twenty five
listings in German (which I do not read), though I do not know if all the
articles are in Czech. Also there was a second reference in one of the model
catalogs (also in German) that listed a mathematician Finsterwalder. He is
also listed on this site though I am unclear if his name was meant to
reference one of the shapes that I am seeking to model. These Model
Catalogues were published by Brill and one by van Dyke in the 1880's.
3. These are amazingly rational and beautiful surfaces, that I would like to
"re-discover". I have seen the Bohemian Dome listed and described in
publications and on the net. I have also photographed a second model that is
star shaped (in a collection in Gottingen), which I have not seen described
anywhere. And I suspect that Sucharda generated other surfaces like this
that were described by "rotating conic sections about conic sections".
4. For my thesis I would like to generate these surfaces from the verbal
descriptions in software that I use in my studies as an architecture
student. If this is not possible I would like to find the equations and
parameters for this series of surfaces that will allow me to generate the
surfaces in Mathematica. Any chance anyone on the list might know someone
who would be willing to help me in this archaeological endeavor? As I am not
a mathematician I am having a little difficulty completing this portion of
my thesis.
Everything else in the project is moving along quite nicely and I am happy
to report that my "geometric intuition" has been proven out over the course
of my readings and research over the past year.
Hoping the list can offer some suggestions.
Regards,
Jonathan Chertok
Austin, Texas
chertok22@hotmail.com
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