<HTML> <!--This file created 20/08/98 0:17 by Claris Home Page version 3.0This file created 20/08/98 0:19 by Claris Home Page version 3.0This file created 20/08/98 21:21 by Claris Home Page version 3.0This file created 21/08/98 10:10 by Claris Home Page version 3.0This file created 21/08/98 16:48 by Claris Home Page version 3.0This file created 23/08/98 15:53 by Claris Home Page version 3.0This file created 24/08/98 11:03 by Claris Home Page version 3.0This file created 24/08/98 15:15 by Claris Home Page version 3.0This file created 24/08/98 15:33 by Claris Home Page version 3.0This file created 24/08/98 21:45 by Claris Home Page version 3.0This file created 25/08/98 9:09 by Claris Home Page version 3.0This file created 25/08/98 9:19 by Claris Home Page version 3.0This file created 25/08/98 9:23 by Claris Home Page version 3.0This file created 25/08/98 9:30 by Claris Home Page version 3.0This file created 25/08/98 9:33 by Claris Home Page version 3.0This file created 25/08/98 9:41 by Claris Home Page version 3.0This file created 25/08/98 9:42 by Claris Home Page version 3.0This file created 25/08/98 10:32 by Claris Home Page version 3.0This file created 25/08/98 10:37 by Claris Home Page version 3.0This file created 27/08/98 16:57 by Claris Home Page version 3.0This file created 30/08/98 10:34 by Claris Home Page version 3.0This file created 30/08/98 11:02 by Claris Home Page version 3.0This file created 30/08/98 19:18 by Claris Home Page version 3.0This file created 31/08/98 22:30 by Claris Home Page version 3.0This file created 1/09/98 7:38 by Claris Home Page version 3.0This file created 1/09/98 8:13 by Claris Home Page version 3.0This file created 2/09/98 8:58 by Claris Home Page version 3.0This file created 3/09/98 7:27 by Claris Home Page version 3.0This file created 5/09/98 21:42 by Claris Home Page version 3.0This file created 5/09/98 22:20 by Claris Home Page version 3.0This file created 5/09/98 22:26 by Claris Home Page version 3.0This file created 6/09/98 8:40 by Claris Home Page version 3.0This file created 6/09/98 8:43 by Claris Home Page version 3.0This file created 6/09/98 21:50 by Claris Home Page version 3.0This file created 7/09/98 8:57 by Claris Home Page version 3.0This file created 7/09/98 9:50 by Claris Home Page version 3.0This file created 7/09/98 9:52 by Claris Home Page version 3.0This file created 8/09/98 8:59 by Claris Home Page version 3.0This file created 14/09/98 9:09 by Claris Home Page version 3.0This file created 14/09/98 17:59 by Claris Home Page version 3.0This file created 18/09/98 22:16 by Claris Home Page version 3.0This file created 18/09/98 22:18 by Claris Home Page version 3.0This file created 18/09/98 22:19 by Claris Home Page version 3.0This file created 29/09/98 1:26 by Claris Home Page version 3.0This file created 29/09/98 1:30 by Claris Home Page version 3.0This file created 29/09/98 1:31 by Claris Home Page version 3.0This file created 29/09/98 1:35 by Claris Home Page version 3.0This file created 3/10/98 17:12 by Claris Home Page version 3.0This file created 10/10/98 18:45 by Claris Home Page version 3.0This file created 20/10/98 12:31 by Claris Home Page version 3.0This file created 20/10/98 12:32 by Claris Home Page version 3.0--> <!--This file created 4/11/98 9:35 by Claris Home Page version 3.0--> <HEAD>    <TITLE>Newsletter on Proof</TITLE>    <META NAME=GENERATOR CONTENT="Claris Home Page 3.0">    <X-CLARIS-WINDOW TOP=42 BOTTOM=680 LEFT=18 RIGHT=973>    <X-CLARIS-TAGVIEW MODE=minimal> </HEAD> <BODY BGCOLOR="#FFFFFF"> <CENTER><IMG SRC="../Images/TitreAnime.gif" WIDTH=553 HEIGHT=97 ALIGN=bottom><FONT SIZE="+1"><B><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0 WIDTH=553>    <TR>       <TD BGCOLOR="#FFFFFF">          <CENTER><FONT SIZE="+1" FACE="Times" COLOR="#666666"><B>Septembre/Octobre          1998</B></FONT></CENTER>       </TD>    </TR> </TABLE> <BR> </B></FONT><IMG SRC="../Images/Nouveautes.gif" WIDTH=553 HEIGHT=34 ALIGN=top></CENTER>  <H2><CENTER><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=5 WIDTH=553>    <TR>       <TD>          <H2><FONT FACE="Times" COLOR="#FF0000">1998</FONT></H2>       </TD>    </TR> </TABLE> <FONT FACE="Times"><TABLE BORDER=0 CELLPADDING=5 WIDTH=552>    <TR>       <TD WIDTH=20>          <P></P>       </TD>       <TD>          <P><FONT FACE="Times" COLOR="#FF0000">Abrougui-Hattab          H.</FONT><FONT FACE="Times"> (1998) <I>La          d&eacute;monstration en g&eacute;om&eacute;trie dans          l'enseignement math&eacute;matique secondaire tunisien</I>.          Th&egrave;se. Grenoble : Universit&eacute; Joseph          Fourier.</FONT></P>       </TD>    </TR>    <TR>       <TD WIDTH=20>          <P><A HREF="http://www.lacim.uqam.ca/pi/indexf.html" TARGET="MAIN_WINDOW"><IMG SRC="../Images/Loupe24.gif" WIDTH=21 HEIGHT=20 BORDER=0 ALIGN=bottom></A></P>       </TD>       <TD>          <P><FONT FACE="Times" COLOR="#FF0000">Delahaye          J.-P.</FONT><FONT FACE="Times"> (1998) Certitudes sans          d&eacute;monstration ? <I>Pour la Science&nbsp;</I>249,          100-105</FONT></P>       </TD>    </TR> </TABLE> &nbsp;</FONT></CENTER></H2>  <CENTER><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=5 WIDTH=553>    <TR>       <TD>          <H2><FONT FACE="Times" COLOR="#FF0000">Archives</FONT></H2>       </TD>    </TR> </TABLE> <FONT FACE="Times"><TABLE BORDER=0 CELLPADDING=5 WIDTH=552>    <TR>       <TD WIDTH=20>          <P><A HREF="http://www.oise.utoronto.ca/~ghanna/synthr5.html"><IMG SRC="../Images/Loupe24.gif" WIDTH=21 HEIGHT=20 BORDER=0 ALIGN=bottom></A></P>       </TD>       <TD>          <P><FONT FACE="Times" COLOR="#FF0000">Akihori          Kanamori</FONT><FONT FACE="Times"> (Guest editor) (1997)          Proof and Progress in Mathematics.<EM> Synthese: An          International Journal for Epistemology, Methodology and          Philosophy of Science</EM>, vol III, 2, May 1997. Dordrecht:          Kluwer Academic Publishers. ISSN 0039-7857, pp.          131-210.</FONT></P>       </TD>    </TR>    <TR>       <TD WIDTH=20>          <P></P>       </TD>       <TD>          <P>&nbsp;</P>       </TD>    </TR> </TABLE>  <IMG SRC="../Images/TraitRouge.gif" WIDTH=553 HEIGHT=6 ALIGN=bottom><IMG SRC="../Images/ThemeFR.gif" WIDTH=548 HEIGHT=33 ALIGN=bottom><TABLE BORDER=0 BGCOLOR="#0099CC" CELLSPACING=0 CELLPADDING=3 WIDTH=553>    <TR>       <TD WIDTH="22%">          <CENTER><A HREF="980910Theme/980910ThemeUK.html"><IMG SRC="../Images/English.gif" WIDTH=53 HEIGHT=17 BORDER=0 ALIGN=bottom></A></CENTER>       </TD>       <TD WIDTH="56%">          <H3><CENTER><FONT FACE="Times">L'affermissement des          d&eacute;monstrations en g&eacute;om&eacute;trie          &eacute;l&eacute;mentaire au tournant du XX&egrave;me          si&egrave;cle</FONT></CENTER></H3>                    <CENTER><FONT FACE="Times">par</FONT>                    <P><FONT FACE="Times"><B>Michel          Guillerault</B></FONT></P></CENTER>       </TD>       <TD WIDTH="22%">          <CENTER><A HREF="980910Theme/980910ThemeES.html"><IMG SRC="../Images/Espanol.gif" WIDTH=74 HEIGHT=16 BORDER=0 ALIGN=bottom></A></CENTER>       </TD>    </TR> </TABLE>  <TABLE BORDER=0 CELLSPACING=0 CELLPADDING=5 WIDTH=549>    <TR>       <TD VALIGN=top>          <P><FONT FACE="Times">Vers la fin du XIX&egrave;me          si&egrave;cle et au d&eacute;but du XX&egrave;me          si&egrave;cle, d&egrave;s M. Pasch et surtout apr&egrave;s          D. Hilbert (Grundlagen der Geometrie, 1899), on se          pr&eacute;occupe d'&eacute;tablir la g&eacute;om&eacute;trie          &eacute;l&eacute;mentaire sur des bases solides, ne faisant          plus implicitement r&eacute;f&eacute;rence aux cas de          figures particuliers qui peuvent se pr&eacute;senter.<BR>          &nbsp;&nbsp;&nbsp;&nbsp;On pr&eacute;sente ici la          contribution &agrave; ce d&eacute;bat d'un relativement          modeste professeur de classes pr&eacute;paratoires aux          Grandes &Eacute;coles fran&ccedil;aises, semble-t-il fort          oubli&eacute; de nos jours, Louis G&eacute;rard, professeur          &agrave; Lyon puis &agrave; Paris, sp&eacute;cialiste de          g&eacute;om&eacute;trie non-euclidienne (Th&egrave;se, 1892)          et fort soucieux de pr&eacute;senter les          th&eacute;or&egrave;mes de g&eacute;om&eacute;trie          &eacute;l&eacute;mentaire de la mani&egrave;re la plus          rigoureuse possible. R&eacute;dacteur du Bulletin de          Sciences math&eacute;matiques et physiques, il y a          publi&eacute; de tr&egrave;s nombreuses notes &agrave; ce          sujet et il est l'auteur (&agrave; l'exception d'une seule)          de toutes les citations qui vont suivre. En particulier , il          est le promoteur infatigable de la notion d'angles          orient&eacute;s de droites, notion qui permet de donner          &agrave; de nombreuses propositions de          g&eacute;om&eacute;trie un caract&egrave;re absolument          g&eacute;n&eacute;ral, ind&eacute;pendant du cas de figure          consid&eacute;r&eacute;...</FONT></P>                    <P><FONT FACE="Times">&nbsp;</FONT></P>                    <CENTER><FONT FACE="Times" COLOR="#0099CC"><B>Pour          continuer</B></FONT><FONT FACE="Times"><BR>          </FONT><A HREF="980910Theme/980910ThemeFR.html"><IMG SRC="../Images/Click.gif" WIDTH=32 HEIGHT=32 BORDER=0 ALIGN=bottom></A>                    <P></P></CENTER>       </TD>    </TR> </TABLE>  </FONT><FONT FACE="Times" COLOR="#FF0000"><IMG SRC="../Images/TraitRouge.gif" WIDTH=553 HEIGHT=6 ALIGN=bottom></FONT>  <P><TABLE BORDER=0 CELLSPACING=4 CELLPADDING=2 WIDTH=553>    <TR>       <TD WIDTH="47%" BGCOLOR="#0099CC">          <CENTER><FONT FACE="Times">Soutenance de th&egrave;se<BR>          </FONT><FONT SIZE="+1" FACE="Times"><B>La          d&eacute;monstration en g&eacute;om&eacute;trie dans          l'enseignement secondaire tunisien<BR>          </B></FONT><FONT FACE="Times">par<B><BR>          Han&egrave;ne Abrougui-Hattab<BR>          </B>Equipe EIAH<BR>          Laboratoire Leibniz, Grenoble</FONT></CENTER>       </TD>       <TD WIDTH="48%" BGCOLOR="#99FF66">          <CENTER><FONT SIZE="+1" FACE="Times"><B>The Pure and the          Applied: Bourbakism Comes to Mathematical Economics<BR>          </B></FONT><FONT FACE="Times">by<BR>          <B>E. Roy Weintraub </B>and <B>Philip Mirowski          </B></FONT></CENTER>       </TD>    </TR>    <TR>       <TD VALIGN=top WIDTH="47%">          <P><FONT FACE="Times">Cette th&egrave;se a pour objectif          d'&eacute;tudier les probl&egrave;mes d'enseignement de la          d&eacute;monstration, en Tunisie. L'&eacute;tude est          organis&eacute;e autour de quatre p&ocirc;les&nbsp;: la          formulation math&eacute;matique, le dessin, l'explication de          la r&egrave;gle de substitution et la strucuture de          l'encha&icirc;nement de la solution. Trois axes de recherche          sont pr&eacute;sent&eacute;s : &eacute;tude de choix          curriculaires, analyse des exigences des enseignants,          &eacute;tude des types d'explication propos&eacute;es par          les &eacute;l&egrave;ves &agrave; propos du passage d'une          hypoth&egrave;se &agrave; une conclusion dans un pas de          d&eacute;monstration.</FONT></P>                    <CENTER><FONT FACE="Times" COLOR="#FF0000">Soutenance le 4          septembre 1998, 15 h.<BR>          Salle Fran&ccedil;ois Jaeger<BR>          Laboratoire Leibniz<BR>          44 avenue F&eacute;lix Viallet, Grenoble</FONT>                    <P><FONT FACE="Times">Renseignements : </FONT><A HREF="mailto:Colette.Laborde@imag.fr"><FONT FACE="Times">Colette          Laborde</FONT></A></P>                    <P></P></CENTER>       </TD>       <TD VALIGN=top ROWSPAN=2 WIDTH="48%">          <P><A HREF="http://www.econ.duke.edu/~erw/Preprints/debreu.bourbaki.html"><FONT FACE="Times"><IMG SRC="../Images/Web.gif" WIDTH=23 HEIGHT=23 BORDER=0 ALIGN=left></FONT></A><FONT FACE="Times">&nbsp;This          paper appeared in a slightly different &nbsp;form &nbsp;in          <I>Science in Context </I>in volume 7, number 2, 1994, pages          245-272. That journal is published by The Cambridge          University Press, which is the copyright holder of          record.</FONT></P>                    <P><FONT FACE="Times"><B>Abstract : </B>In the minds of          many, the Bourbakist trend in mathematics was characterized          by pursuit of rigor to the detriment of concern for          applications or didactic concessions to the non-          mathematician, which would seem to render the concept of a          Bourbakist incursion into a field of applied mathematics an          oxymoron. We argue that such a conjuncture did in fact          happen in postwar mathematical economics, and describe the          career of Gerard Debreu in order to illustrate how it          happened. Using the work of Leo Corry on the fate of the          Bourbakist program in mathematics, we demonstrate that many          of the same problems of the search for a formal structure          with which to ground mathematical practice also happened in          the case of Debreu. We view this case study as an          alternative exemplar to conventional discussions concerning          the "unreasonable effectiveness" of mathematics in          science.<BR>          </FONT></P>       </TD>    </TR>    <TR>       <TD WIDTH="47%" BGCOLOR="#99FF66">          <CENTER><FONT SIZE="+1" FACE="Times"><B>On the nature of          mathematical concepts<BR>          </B></FONT><FONT FACE="Times">by<BR>          <B>Verena Huber-Dyson</B></FONT></CENTER>       </TD>    </TR>    <TR>       <TD VALIGN=top WIDTH="47%">          <P><A HREF="http://www.edge.org/3rd_culture/huberdyson/index.html"><IMG SRC="../Images/Web.gif" WIDTH=23 HEIGHT=23 BORDER=0 ALIGN=left></A>&nbsp;&nbsp;This          on-line paper may provide the reader a &nbsp;&nbsp;new view          on a classical question which is at the core of research on          mathematics education.</P>       </TD>       <TD WIDTH="48%" BGCOLOR="#99FF66">          <CENTER><FONT SIZE="+1" FACE="Times"><B>An Interactive Proof          of<BR>          Pythagoras' theorem</B></FONT></CENTER>       </TD>    </TR>    <TR>       <TD VALIGN=top WIDTH="47%">          <P>The title could have been, <I>On the nature of          mathematical truth</I>, a permanent question for the reader          of the proof newsletter...</P>                    <P>This paper was also my starting point for the discovery          of the <I>Edge Third Culture</I> website. I recommend it to          the reader. (NB)</P>       </TD>       <TD VALIGN=top WIDTH="48%">          <P><A HREF="http://SunSITE.UBC.CA/LivingMathematics/V001N01/UBCExamples/Pythagoras/pythagoras.html"><FONT FACE="Times"><IMG SRC="../Images/Web.gif" WIDTH=23 HEIGHT=23 BORDER=0 ALIGN=left></FONT></A><FONT FACE="Times">&nbsp;Click          on "Web" and discover a Java applet &nbsp;presenting an          interactive proof of Pythagoras theorem. This Java applet          was written by Jim Morey, it won grand prize in Sun          Microsystem's Java programming contest in the Summer of          1995.</FONT></P>                    <CENTER><FONT FACE="Times">An interactive proof can also be          experienced in the </FONT><A HREF="970506.html"><FONT FACE="Times">mai/juin          1997 Proof Newsletter</FONT></A></CENTER>       </TD>    </TR> </TABLE> </P>  <P><IMG SRC="../Images/TraitRouge.gif" WIDTH=553 HEIGHT=6 ALIGN=bottom><TABLE BORDER=0 CELLPADDING=10 WIDTH=553>    <TR>       <TD WIDTH=310>          <P><IMG SRC="../Images/LogoICME9.gif" WIDTH=304 HEIGHT=253 ALIGN=left></P>       </TD>       <TD VALIGN=top>          <CENTER><FONT SIZE="+2" FACE="Times"><B>FIRST          ANNOUNCEMENT</B></FONT></CENTER>                    <P><FONT FACE="Times">&nbsp;</FONT></P>                    <P><FONT FACE="Times">The National Organizing Committee for          the 9th International Congress on Mathematical Education          (ICME9) on behalf of the International Commission on          Mathematical Instruction (ICMI), is pleased to announce that          ICME9 will be held in Tokyo/Makuhari, Japan, from July 31 to          August 6, 2000. Makuhari is located between the center of          Tokyo and Tokyo International Airport (Narita).</FONT></P>                    <P><FONT SIZE="+1" FACE="Times"><B>E-mail:<BR>          </B></FONT><A HREF="mailto:icme9@ma.kagu.sut.ac.jp"><FONT FACE="Times">icme9@ma.kagu.sut.ac.jp</FONT></A></P>                    <P><FONT SIZE="+1" FACE="Times"><B>URL:<BR>          </B></FONT><A HREF="http://www.ma.kagu.sut.ac.jp/~icme9/"><FONT FACE="Times">http://www.ma.kagu.sut.ac.jp/~icme9/</FONT></A></P>       </TD>    </TR>    <TR>       <TD COLSPAN=2>          <P><FONT FACE="Times">In the programme preview one will          notice a Topic Study Group (TSG) on proof :</FONT></P>                    <CENTER><FONT SIZE="+1" FACE="Times" COLOR="#FF0033"><B>TSG          12: Proof and Proving in Mathematics Education</B></FONT>                    <P><FONT FACE="Times">be ready... pre-register          !</FONT></P></CENTER>                    <P><FONT FACE="Times">Send the following information to the          ICME9 secretariat :</FONT></P>                    <BLOCKQUOTE><BLOCKQUOTE><FONT FACE="Times">Prof./Dr./Mr./Ms.<BR>                Female/Male<BR>                Name (family name) (first name) (middle name)<BR>                Affiliation<BR>                Mailing Address<BR>                Postal Code<BR>                Country<BR>                Telephone number<BR>                Fax number<BR>                E-mail address</FONT></BLOCKQUOTE></BLOCKQUOTE>       </TD>    </TR> </TABLE>  <IMG SRC="../Images/TraitRouge.gif" WIDTH=553 HEIGHT=6 ALIGN=bottom></P>  <P><FONT SIZE="+1"><B><TABLE BORDER=0 CELLSPACING=4 CELLPADDING=5 WIDTH=553>    <TR>       <TD WIDTH=265 BGCOLOR="#3366CC">          <H1><CENTER><FONT FACE="Times"><B>Tigre</B></FONT></CENTER></H1>       </TD>       <TD VALIGN=top WIDTH=265 BGCOLOR="#99FF66">          <CENTER><FONT SIZE="+1"><B>What is a          calculation?</B></FONT><BR>          by<BR>          <B>O. Bradley Bassler</B></CENTER>       </TD>    </TR>    <TR>       <TD WIDTH=265>          <P><A HREF="http://www.irisa.fr/repco/Pages_Pros/py/Tigre/Welcome.html"><FONT FACE="Times"><B><IMG SRC="../Images/tigre.gif" WIDTH=64 HEIGHT=59 BORDER=0 ALIGN=left></B></FONT></A><FONT FACE="Times">Tigre          est un logiciel d'aide &agrave; l'apprentissage de la          d&eacute;monstration en g&eacute;om&eacute;trie, au niveau          coll&egrave;ge, d&eacute;velopp&eacute; par </FONT><A HREF="mailto:py@irisa.fr?Subject=Tigre"><FONT FACE="Times">Dominique          Py</FONT></A><FONT FACE="Times">. Il comprend: un logiciel          &eacute;l&egrave;ve (Tigre), un logiciel professeur          (TigreP), une base de th&eacute;or&egrave;mes et une base          d'exercices.<BR>          &nbsp;&nbsp;&nbsp;Cliquer sur le Tigre pour en savoir          plus...</FONT></P>                    <P><FONT FACE="Times"><I>Tigre peut &ecirc;tre librement          diffus&eacute;, recopi&eacute; et utilis&eacute; &agrave;          des fins d'enseignement et de recherche, en dehors de toute          exploitation commerciale. </I></FONT></P>       </TD>       <TD VALIGN=top WIDTH=265>          <P><A HREF="http://jwilson.coe.uga.edu/DEPT/Mesa/Bassler/Acalcu.html"><FONT FACE="Times"><IMG SRC="../Images/Web.gif" WIDTH=23 HEIGHT=23 BORDER=0 ALIGN=left></FONT></A><FONT FACE="Times">&nbsp;This          is the text of a talk to a </FONT>MESA<BR>          &nbsp;(Mathematics Education Student Association) colloquium          <FONT FACE="Times">at the University of Georgia (Department          of Mathematics Education) on November 12, 1997.<BR>          </FONT>&nbsp;&nbsp;<FONT FACE="Times">In this paper the          author suggests "an alternative view of calculation which          would not be restricted to 'effective' or 'mechanical'          calculation, but which may or may not encompass all          varieties of 'machine calculation'."</FONT></P>                    <CENTER><FONT FACE="Times">More information about MESA          colloquium, visit<BR>          </FONT><A HREF="http://jwilson.coe.uga.edu"><FONT FACE="Times">Jim          Wilson site</FONT></A></CENTER>       </TD>    </TR>    <TR>       <TD COLSPAN=2 WIDTH=530 BGCOLOR="#99FF66">          <CENTER><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0 WIDTH=549>             <TR>                <TD WIDTH=84>                   <P><A HREF="http://forum.swarthmore.edu/electronic.newsletter/"><FONT COLOR="#00AF00"><IMG SRC="../Images/MathForum.gif" WIDTH=73 HEIGHT=61 BORDER=0 ALIGN=bottom></FONT></A></P>                </TD>                <TD>                   <CENTER><FONT COLOR="#00AF00">from&nbsp;<B>THE MATH                   FORUM INTERNET NEWS<BR>                   31 August 1998, Vol.3, No.35</B></FONT></CENTER>                </TD>             </TR>          </TABLE>           <FONT COLOR="#00AF00">&nbsp;</FONT><FONT SIZE="+1"><B> The          Kepler Conjecture</B></FONT><B><BR>          </B>by<BR>          <B>Thomas C. Hales, Samuel P. Ferguson<BR>          </B></CENTER>       </TD>    </TR>    <TR>       <TD COLSPAN=2 WIDTH=530>          <P>In a booklet published in 1611, J. Kepler described the          arrangement of equal spheres into the familiar cannonball          arrangement. He asserted that</P>                    <BLOCKQUOTE>"The packing will be the tightest possible, so             that in no other arrangement could more pellets be             stuffed into the same container."</BLOCKQUOTE>                    <P>Thomas Hales and Samuel Ferguson claim to have proved the          Kepler Conjecture, that no packing of equal-sized spheres in          space can have greater density than that of the          face-centered-cubic packing.</P>                    <P><A HREF="http://www.math.lsa.umich.edu/~hales/countdown/"><IMG SRC="../Images/Web.gif" WIDTH=23 HEIGHT=23 BORDER=0 ALIGN=left></A>&nbsp;&nbsp;The          full proof is included in postscript format, as well as some          background, history, popular and &nbsp;&nbsp;academic          articles, a link to the "serious stuff" for discrete          geometers who wish to check the technical details of the          solution, and links to the software used.</P>                    <P></P>       </TD>    </TR> </TABLE>  <TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0 WIDTH=553>    <TR>       <TD>          <P><IMG SRC="../Images/TraitRouge.gif" WIDTH=553 HEIGHT=6 BORDER=0 ALIGN=middle></P>       </TD>    </TR> </TABLE>  </B></FONT><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0 WIDTH=553>    <TR>       <TD VALIGN=top>          <CENTER><IMG SRC="../Images/Services.gif" WIDTH=553 HEIGHT=27 BORDER=0 ALIGN=middle><TABLE BORDER=0 BGCOLOR="#CCCCCC" CELLSPACING=0 CELLPADDING=10 WIDTH=553>             <TR>                <TD>                   <CENTER><A HREF="../indexFR.html"><FONT FACE="Times" COLOR="#0033CC"><B>La                   bibliographie</B></FONT></A><FONT FACE="Times" COLOR="#0033CC"><B><BR>                   </B></FONT><A HREF="../SearchIndex/AT-preuvequery.html"><FONT FACE="Times" COLOR="#0033CC"><B>Outil                   de recherche</B></FONT></A><FONT FACE="Times" COLOR="#0033CC"><B><BR>                   Cours en ligne<BR>                   Questions et r&eacute;ponses</B></FONT>                                      <P><A HREF="../PreuveAvertFR.html"><FONT FACE="Times" COLOR="#0033CC"><B>A                   propos du site</B></FONT></A></P></CENTER>                </TD>                <TD>                   <CENTER><A HREF="../indexUK.html"><FONT FACE="Times" COLOR="#00CC00"><B>The                   bibliography</B></FONT></A><FONT FACE="Times" COLOR="#00CC00"><B><BR>                   </B></FONT><A HREF="../SearchIndex/AT-preuvequery.html"><FONT FACE="Times" COLOR="#00CC00"><B>Search                   tool</B></FONT></A><FONT FACE="Times" COLOR="#00CC00"><B><BR>                   Online course<BR>                   Questions and answers</B></FONT>                                      <P><A HREF="../PreuveAvertUK.html"><FONT FACE="Times" COLOR="#00CC00"><B>About                   the site</B></FONT></A></P></CENTER>                </TD>                <TD>                   <CENTER><A HREF="../indexES.html"><FONT FACE="Times" COLOR="#FF6600"><B>La                   bibliografia</B></FONT></A><FONT FACE="Times" COLOR="#FF6600"><B><BR>                   </B></FONT><A HREF="../SearchIndex/AT-preuvequery.html"><FONT FACE="Times" COLOR="#FF6600"><B>Herramienta                   de busqueda</B></FONT></A><FONT FACE="Times" COLOR="#FF6600"><B><BR>                   Curso electronico<BR>                   Preguntas y repuestas</B></FONT>                                      <P><A HREF="../PreuveAvertES.html"><FONT FACE="Times" COLOR="#FF6600"><B>Con                   respecto a este                   servidor</B></FONT></A></P></CENTER>                </TD>             </TR>          </TABLE>           <IMG SRC="../Images/Sugestions.gif" WIDTH=553 HEIGHT=27 BORDER=0 ALIGN=top><TABLE BORDER=0 BGCOLOR="#CCCCCC" CELLSPACING=0 CELLPADDING=10 WIDTH=553>             <TR>                <TD WIDTH=309>                   <P ALIGN=right><FONT FACE="Times" COLOR="#0000CC"><B>Adresser                   suggestions et remarques                   &agrave;...</B></FONT><FONT FACE="Times" COLOR="#FF0000"><B><BR>                   </B></FONT><FONT FACE="Times" COLOR="#00CC00"><B>Send                   remarks and suggestions to...<BR>                   </B></FONT><FONT FACE="Times" COLOR="#FF6600"><B>Enviar                   comentarios y sugerencias a ...</B></FONT></P>                </TD>                <TD ALIGN=center>                   <P ALIGN=left><B><IMG SRC="../Images/Lettre50.gif" WIDTH=38 HEIGHT=28 BORDER=0 ALIGN=middle>&nbsp;</B><A HREF="mailto:Nicolas.Balacheff@imag.fr?Subject=ProofNewsletter"><FONT FACE="Times"><B>The                   newsletter editor</B></FONT></A></P>                </TD>             </TR>          </TABLE>           <IMG SRC="../Images/PastNewsletters.gif" WIDTH=552 HEIGHT=26 BORDER=0 ALIGN=middle><TABLE BORDER=0 BGCOLOR="#CCCCCC" CELLSPACING=0 CELLPADDING=5 WIDTH=553>             <TR>                <TD>                   <P></P>                </TD>             </TR>          </TABLE>                    <TABLE BORDER=0 BGCOLOR="#CCCCCC" CELLSPACING=0 CELLPADDING=5 WIDTH=553>             <TR>                <TD>                   <P><FONT FACE="Times" COLOR="#AF0000">1415</FONT><FONT FACE="Times">                   &#91;</FONT><A HREF="980708.html"><FONT FACE="Times">98                   07/08</FONT></A><FONT FACE="Times">&#93;                   &#91;</FONT><A HREF="980506.html"><FONT FACE="Times">98                   05/06</FONT></A><FONT FACE="Times">&#93;                   &#91;</FONT><A HREF="980304.html"><FONT FACE="Times">98                   03/04</FONT></A><FONT FACE="Times">&#93;                   &#91;</FONT><A HREF="980102.html"><FONT FACE="Times">98                   01/02</FONT></A><FONT FACE="Times">&#93;                   </FONT><FONT FACE="Times" COLOR="#AF0000">1629</FONT><FONT FACE="Times" COLOR="#FFFF33">                   </FONT><FONT FACE="Times">&#91;</FONT><A HREF="971112.html"><FONT FACE="Times">97                   11/12</FONT></A><FONT FACE="Times">&#93;                   &#91;</FONT><A HREF="970910.html"><FONT FACE="Times">97                   09/10</FONT></A><FONT FACE="Times">&#93;                   &#91;</FONT><A HREF="970708.html"><FONT FACE="Times">97                   07/08</FONT></A><FONT FACE="Times">&#93;                   &#91;</FONT><A HREF="970506.html"><FONT FACE="Times">97                   05/06</FONT></A><FONT FACE="Times">&#93;                   &#91;</FONT><A HREF="970304.html"><FONT FACE="Times">97                   03/04</FONT></A><FONT FACE="Times">&#93;<BR>                   &#91;</FONT><A HREF="970102.html"><FONT FACE="Times">97                   01/02</FONT></A><FONT FACE="Times">&#93;</FONT></P>                </TD>             </TR>          </TABLE>           <IMG SRC="../Images/TraitRouge.gif" WIDTH=553 HEIGHT=6 BORDER=0 ALIGN=bottom><TABLE BORDER=0 BGCOLOR="#AEAEAE" CELLSPACING=0 CELLPADDING=5 WIDTH=553>             <TR>                <TD WIDTH="30%">                   <CENTER><FONT FACE="Times"><IMG SRC="../Images/LogoLeibniz.gif" WIDTH=132 HEIGHT=69 BORDER=0 ALIGN=bottom><BR>                   </FONT><A HREF="http://www.leibniz.imag.fr"><FONT FACE="Times" COLOR="#000033"><B>Laboratoire                   Leibniz</B></FONT></A></CENTER>                </TD>                <TD WIDTH="45%">                   <P>&nbsp;&nbsp;&nbsp;&nbsp;</P>                </TD>                <TD WIDTH="25%">                   <CENTER><IMG SRC="../Images/Logo%20Cabri.gif" WIDTH=61 HEIGHT=35 BORDER=0 ALIGN=bottom>                                      <P><A HREF="http://www-cabri.imag.fr"><FONT FACE="Times" COLOR="#000000"><B>Projet                   Cabri-g&eacute;om&egrave;tre</B></FONT></A></P></CENTER>                </TD>             </TR>          </TABLE>                    <TABLE BORDER=0 BGCOLOR="#CCCCCC" CELLSPACING=0 CELLPADDING=5 WIDTH=553>             <TR>                <TD>                   <CENTER><FONT FACE="Times">Editeur :                   </FONT><A HREF="mailto:Nicolas.Balacheff@imag.fr?Subject=ProofNewsletter"><FONT FACE="Times"><B>Nicolas                   Balacheff</B></FONT></A><FONT FACE="Times"><B><BR>                   </B>English Editor : </FONT><A HREF="mailto:warfield@math.washington.edu?Subject=ProofNewsletter"><FONT FACE="Times"><B>Virginia                   Warfield</B></FONT></A><FONT FACE="Times">, Editor                   en Castellano <B>: </B></FONT><A HREF="mailto:patricio@coe.uga.edu?Subject=ProofNewsletter"><FONT FACE="Times"><B>Patricio                   Herbst</B></FONT></A>                                      <P><FONT FACE="Times">Comit&eacute; scientifique                   :<B> </B></FONT><A HREF="mailto:dchazan@pilot.msu.edu?Subject=ProofNewsletter"><FONT FACE="Times"><B>Daniel                   Chazan</B></FONT></A><FONT FACE="Times"><B>,                   </B></FONT><A HREF="mailto:rayduval@gat.univ-lille1.fr?Subject=ProofNewsletter"><FONT FACE="Times"><B>Raymond                   Duval</B></FONT></A><FONT FACE="Times"><B>,                   </B></FONT><A HREF="mailto:ghanna@oise.utoronto.ca?Subject=ProofNewsletter"><FONT FACE="Times"><B>Gila                   Hanna</B></FONT></A><FONT FACE="Times"><B>,                   </B></FONT><A HREF="mailto:harel@math.purdue.edu?Subject=ProofNewsletter"><FONT FACE="Times"><B>Guershon                   Harel</B></FONT></A><FONT FACE="Times"><B>,<BR>                   </B></FONT><A HREF="mailto:choyles@ioe.ac.uk?Subject=ProofNewsletter"><FONT FACE="Times"><B>Celia                   Hoyles</B></FONT></A><FONT FACE="Times"><B>,                   </B></FONT><A HREF="mailto:mariotti@gauss.dm.unipi.it?Subject=ProofNewsletter"><FONT FACE="Times"><B>Maria-Alessandra                   Mariotti</B></FONT></A><FONT FACE="Times"><B>,                   </B></FONT><A HREF="mailto:motte@meller-netz.de?Subject=ProofNewsletter"><FONT FACE="Times"><B>Michael                   Otte</B></FONT></A><FONT FACE="Times"><B>,                   </B></FONT><A HREF="mailto:profmd@mweb.co.za?Subject=ProofNewsletter"><FONT FACE="Times"><B>Michael                   de Villiers</B></FONT></A></P>                                      <P></P></CENTER>                </TD>             </TR>          </TABLE>          </CENTER>       </TD>    </TR> </TABLE> </P></CENTER> </BODY> </HTML> 
