{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 13 256 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 3 "" 0 "" {TEXT -1 44 "3D plot of the torus with \+ some marked curves" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 52 "We define the torus implicitly, as the locus where \n" } {XPPEDIT 18 0 "(sqrt(x^2+z^2)-2)^2 + y^2 = 1" "6#/,&*$,&-%%sqrtG6#,&*$ %\"xG\"\"#\"\"\"*$%\"zGF-F.F.F-!\"\"F-F.*$%\"yGF-F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "pic4;" }}{PARA 256 "" 1 "" {GLPLOT3D 496 496 496 {PLOTDATA 3 "6*-%'CURVESG6%7T7%$\"\"$\"\"!$F*F*F +7%$\"+9+z\"*H!\"*$\"+<;xy7!#5F+7%$\"+j[HnHF/$\"+SeaODF2F+7%$\"+dn\"p# HF/$\"+\\+n_PF2F+7%$\"+/(=8(GF/$\"+@b<2\\F2F+7%$\"+AOT,GF/$\"+1`5\")fF 2F+7%$\"+]$\\$=FF/$\"+2b#o&pF2F+7%$\"+-)*[BEF/$\"+E[J=yF2F+7%$\"+oDR=D F/$\"+KwU^&)F2F+7%$\"+ULy/CF/$\"+Li7W\"*F2F+7%$\"+&eFXG#F/$\"+M&yme*F2 F+7%$\"+$*)*ff@F/$\"+Py\"=()*F2F+7%$\"+v:0K?F/$\"+j@'[***F2F+7%$\"+sp( R!>F/$\"+F6z`**F2F+7%$\"+j!zux\"F/$\"+:\"z#\\(*F2F+7%$\"+U\\ja;F/$\"+4 Uo%Q*F2F+7%$\"+1;\"F/ $\"+m*[`X&F2F+7%$\"+I6.*4\"F/$\"+Qt$)QVF2F+7%$\"+^U%40\"F/$\"+?@3^JF2F +7%$\"+U3W=5F/$\"+@ie6>F2F+7%$\"+2Y0-5F/$\"+!G@qS'!#6F+7%$\"+3Y0-5F/$! +fF-2kF`sF+7%$\"+X3W=5F/$!+mje6>F2F+7%$\"+cU%40\"F/$!+hA3^JF2F+7%$\"+O 6.*4\"F/$!+ru$)QVF2F+7%$\"++>\">;\"F/$!+!4\\`X&F2F+7%$\"+[SbQ7F/$!+FSG #['F2F+7%$\"+<\"*pF8F/$!+R+y-uF2F+7%$\"+\\L)yU\"F/$!+2Es,#)F2F+7%$\"+? 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generate four separate plots of the curves that we want\n# to mark in red on the surface of the torus.\nCurve1 :=\n spacecurve([cos (t)+2,sin(t),0],t=0..2*Pi,color=red,thickness=2):\nCurve2 :=\n spacecu rve([cos(t)-2,sin(t),0],t=0..2*Pi,color=red,thickness=2):\nCurve3 :=\n spacecurve([2*cos(t),1,2*sin(t)],t=0..2*Pi,color=red,thickness=2):\nC urve4 :=\n spacecurve([2*cos(t),-1,2*sin(t)],t=0..2*Pi,color=red,thick ness=2):\n\n# Combine all the elements.\npic4 := \n display(\n Curve1 ,\n Curve2,\n Curve3,\n Curve4,\n Torus,\n axes=boxed, \+ # enclose in a box\n scaling=constrained, # use the same scaling for all 3 axes\n labels=['x','y','z'] # label the axes\n ):\n" }} }}}{MARK "3" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }