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-1 26 "Stability of the catenoid." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 332 "These pictures are related to the formul
a for the second variation of area, but reasoning is ommitted.  The va
riations indicated by the first picture (from the point where the vari
ation is zero) indicate a direction of instability, i.e. a way for the
 surface to decrease its surface area.  This causes the critical  cate
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{XPPMATH 20 "6#-%'RootOfG6#,**&%#_ZG\"\"\")-%$expG6#F(\"\"#F)F)F(!\"\"
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ed circular radius at the top and bottom\n  #this is the \"tallest\" c
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{MPLTEXT 1 0 147 "plot3d([cosh(t)*sin(theta),cosh(t)*cos(theta),t],t=-
2..2,\ntheta=0..2*Pi,title=\"post-critical catenoid\");\n  #you won't \+
see this fellow sitting still" }}{PARA 13 "" 1 "" {GLPLOT3D 400 300 
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