Editing 3Dconfigurations/RiemannEllipsoids (section)

=Riemann (1826 - 1866)=

==Background==

Excerpt from p. 539 of R. Baker, C. Christenson &amp; H. Orde (2004):
<table border="0" width="90%" align="center"><tr><td align="left">
<font color="darkgreen">"Newton first showed that the departure of the figure of the earth from a sphere is due to its rotation.  Jacobi showed in 1834 that gravitational equilibrium of a rotating spheroid is consistent with three distinct axes if the angular momentum exceeds a critical value.  Dirichlet had posed and partially analyzed the conditions for a configuration which is an ellipsoid varying with time, such that the motion in an inertial frame, is linear in the coordinates.  His results were edited posthumously by Dedekind in 1860.</font>  In his published work dated 1861 &#8212; five years before his death &#8212; <font color="darkgreen">Riemann took up this problem of Dirichlet &hellip;"</font>
</td></tr></table>

Excerpt from p. 530 of R. Baker, C. Christenson &amp; H. Orde (2004) which, in turn, is taken from R. Dedekind's accounting of ''The life of Bernhard Riemann'':

<table border="0" width="90%" align="center"><tr><td align="left">
<font color="darkgreen">"In the Easter vacation of 1860 [Riemann] went on a trip to Paris, where he stayed for a month from 26th March; unfortunately the weather was raw and unfriendly and in the last week of his visit there was one day after another of snow and hail which made it almost impossible to see the sights.  However, he was delighted with the friendly reception which he received from the Parisian scholars Serret, Bertrand, Hermite, Puiseux and Briot, with whom he spent a pleasant day in the country at Chatenay, along with Bouquet.  In the same year, [Riemann] completed his paper on the motion of a fluid ellipsoid &hellip;"</font>
</td></tr></table>

Excerpt from pp. 184-185 of EFE:

<table border="0" width="90%" align="center"><tr><td align="left">
<font color="lightblue">"Riemann's paper 'Ein Beitrag zu den Untersuchungen &uuml;ber die Bewegung eines fl&uuml;ssigen gleichartigen Ellipsoides,' communicated to ''Der K&ouml;niglichen Gesellschaft der Wissenschaften zu G&ouml;ttingen'' on December 8, 1860, is remarkable for the wealth of new results it contains and for the breadth of its comprehension of the entire range of problems.  In the present writer's [S. Chandrasekhar] view this much neglected paper &#8212;</font> [for example] <font color="lightblue">there are no references to it in any of the writings of Poincar&eacute;, Darwin, or Jeans &#8212; deserves to be included among the other great papers of Riemann that are well known.   &hellip;  In view of Riemann's unique place in science, a critical appraisal of this paper is perhaps justified."
</font>
</td></tr></table>

==His Published Work on Ellipsoids==
Riemann's (1861) work, titled, "Ein Beitrag zu den Untersuchungen &uuml;ber die Bewegung eines fl&uuml;ssigen gleichartigen Ellipsoides" &#8212; English translation: "A contribution to the study of the motion of a homogeneous fluid ellipsoid" &#8212; can be found in various published collections of his papers:
<ul>
<li>In the German language: &nbsp; [https://books.google.com/books?id=vo9VAAAAYAAJ&pg=PR6&dq=Gesammelte+Mathematische+Werke+B.+Riemann&source=gbs_selected_pages&cad=3#v=onepage&q=Gesammelte%20Mathematische%20Werke%20B.%20Riemann&f=false Bernhard Riemann (1876)] ''Gesammelte Mathematische Werke und Wissenschaftlicher'', especially Chapter X (p. 168).
</li>
<li>In the German language: &nbsp; "Bernhard Riemann's Gesammelte Mathematische Werke," 2<sup>nd</sup> edition, edited by Heinrich Weber, Teubner, Leipzig, 1892.</li>
<li>In English (referred to below as BCO2004): &nbsp; [http://www.kendrickpress.com/Riemann.htm "Bernhard Riemann Collected Papers," translated by Roger Baker, Charles Christenson and Henry Orde] from the 1892 (German) edition and published in 2004 (Heber City, Utah, USA: Kendrick Press).
</ul>
Our description and detailed analysis of Riemann's (1861) work that follows, draws primarily from the 2004 translation of his collected works.