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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 127 "Here are the three equati
ons that (parametrically) generate the umbilic torus that appears on t
he cover of our Cal I text book:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 45 "z := sin(u)*((7.+cos(u/3-2*v)+2*cos(u/3+v)));" }
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "y := cos(u)
*((7.+cos(u/3-2*v)+2*cos(u/3+v)));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 34 "x := sin(u/3-2*v) + 2.*sin(u/3+v);" }{TEXT -1 0 "" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "for i to 12 do p.i:=plot3d(
[x,y,z],u=-Pi..Pi,v=-Pi..Pi,orientation=[30*i,90]) od:" }{TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "plots[display]([seq(p.i
,i=1..12)],insequence=true);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 90 "You could do it this way: multiply your parametric expr
essions by the 3x3 rotation matrix " }{XPPEDIT 18 0 "matrix([[cos(k), \+
sin(k), 0], [-sin(k), cos(k), 0], [0, 0, 1]]);" "6#-%'matrixG6#7%7%-%$
cosG6#%\"kG-%$sinG6#F+\"\"!7%,$-F-6#F+!\"\"-F)6#F+F/7%F/F/\"\"\"" }
{TEXT -1 2 ". " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "plots[ani
mate3d]([cos(k)*x+sin(k)*y,-sin(k)*x+cos(k)*y,z],u=-Pi..Pi,v=-Pi..Pi,k
=-Pi..Pi);" }{TEXT -1 0 "" }}}}{MARK "0 0 0" 127 }{VIEWOPTS 1 1 0 1 1 
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