<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><br><div> <span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font face="Helvetica" size="3" style="font: normal normal normal 12px/normal Helvetica; "><br class="Apple-interchange-newline">Zbigniew Nitecki</font></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font face="Helvetica" size="3" style="font: normal normal normal 12px/normal Helvetica; ">Department of Mathematics</font></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font face="Helvetica" size="3" style="font: normal normal normal 12px/normal Helvetica; ">Tufts University</font></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font face="Helvetica" size="3" style="font: normal normal normal 12px/normal Helvetica; ">Medford, MA 02155</font></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Helvetica; min-height: 14px; "><br></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font face="Helvetica" size="3" style="font: normal normal normal 12px/normal Helvetica; ">telephones:</font></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font face="Helvetica" size="3" style="font: normal normal normal 12px/normal Helvetica; ">Office<span class="Apple-converted-space"><span class="Apple-converted-tab"> <span class="Apple-converted-space"> </span></span></span>(617)627-3843</font></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font face="Helvetica" size="3" style="font: normal normal normal 12px/normal Helvetica; ">Dept.<span class="Apple-converted-space"><span class="Apple-converted-tab"> <span class="Apple-converted-space"> </span></span></span>(617)627-3234</font></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font face="Helvetica" size="3" style="font: normal normal normal 12px/normal Helvetica; ">Dept. fax<span class="Apple-converted-space"><span class="Apple-converted-tab"> <span class="Apple-converted-space"> </span></span></span>(617)627-3966</font></p><a href="http://www.tufts.edu/~znitecki/">http://www.tufts.edu/~znitecki/</a></span> </div><br><div><div>On Jan 11, 2009, at 10:10, Jean-Paul Vignault wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; ">\begin{pspicture}(-6,-3)(6,3)<br><br>\defFunction{mobius}(u,v)<br>{2 u v Cos mul add 2 v mul Cos mul}<br>{2 u v Cos mul add 2 v mul Sin mul}<br>{u v Sin mul}<br><br>\defFunction{centercircle}(t)<br>{2 t mul Cos 2 mul}<br>{2 t mul Sin 2 mul}<br>{0}<br><br>\psset[pst-solides3d]{viewpoint=20 10 15,Decran=40,lightsrc=10 20 10}<br>\psSolid[object=courbe,<br>range= 0 pi,<br>linewidth=1.5\pslinewidth,<br>linecolor=blue,<br>function=centercircle,<br>ngrid=1,r=0]<br><br>\psSolid[object=surfaceparametree, linewidth=0.5\pslinewidth,<br>base=-0.4 0.4 0 pi, fillcolor=lightgray!30, incolor=white,<br>function=mobius,<br>name=Band,<br>ngrid=.05]<br><br>\codejps{<br>%.8 setgray %% linecolor<br>Band<br>-0.35 0.35 3.5 {<br> /rv exch def<br> rv Sin rv 2 mul Cos mul neg<br> rv Sin rv 2 mul Sin mul neg<br> rv Cos<br> newvecteur<br> {rv 2 mul Cos 2 mul<br> rv 2 mul Sin 2 mul<br> 0<br> addv3d<br> } solidtransform<br> dup (.8 setgray) solidputcolors<br> solidfuz<br>} for<br>draw**<br>}<br>\end{pspicture}<br></span></blockquote></div><br></div></body></html>