{VERSION 1 0 "X11/Motif" "1.0"}{GLOBALS 3 1}{FONT 0 "-adobe-helve
tica-bold-r-normal--*-180-*-*-*-*-*-*" "helvetica" "Helvetica-Bol
d" 8 18 0 "Helvetica-Bold" 18}{FONT 1 "-adobe-new century schoolb
ook-bold-i-normal--*-180-*-*-*-*-*-*" "new century schoolbook" "T
imes-BoldItalic" 8 18 96 "Times-BoldItalic" 18}{FONT 2 "-adobe-co
urier-medium-r-normal--*-140-*" "courier" "Courier" 4 14 192 "Cou
rier" 12}{FONT 3 "-adobe-helvetica-bold-r-normal--*-240-*-*-*-*-*
-*" "helvetica" "Helvetica-Bold" 8 24 0 "Helvetica-Bold" 24}{FONT
 4 "-adobe-helvetica-bold-r-normal--*-240-*-*-*-*-*-*" "helvetica
" "Helvetica-Bold" 8 24 0 "Helvetica-Bold" 24}{FONT 5 "-adobe-hel
vetica-bold-r-normal--*-240-*-*-*-*-*-*" "helvetica" "Helvetica-B
old" 8 24 0 "Helvetica-BoldOblique" 24}{FONT 6 "-adobe-helvetica-
bold-r-normal--*-240-*-*-*-*-*-*" "helvetica" "Helvetica-Bold" 8 
24 0 "Helvetica-Bold" 24}{FONT 7 "-adobe-helvetica-bold-r-normal-
-*-140-*" "helvetica" "Helvetica-Bold" 8 14 0 "Helvetica-Bold" 14
}{SCP_R 1 0 51{COM_R 2 0{TEXT 1 142 "Gabor Toth: Animations.\015\
015 The following  Maple file creates some animated graphics used
 in `Glimpses of Algebra and Geometry', Springer, 1977."}}{SEP_R 
3 0}{COM_R 4 0{TEXT 1 57 "The Mobius strip is traced by a segment
  moving in space."}}{SEP_R 5 0}{INP_R 6 0 "> "{TEXT 0 222 "with(
plots):animate3d(\012[cos(t*u)*(2+v*cos(t*u/2)),sin(t*u)*(2+v*cos
(t*u/2)),v*sin(t*u/2)],\012u=0..2*Pi,v=-1..1,t=0..1,\012thickness
=3,color=v,style=patchnogrid,scaling=constrained,axes=none,\012ti
tle=`Animating the Mobius Strip`);"}}{SEP_R 7 0}{COM_R 8 0{TEXT 1
 67 "Flattening out a sphere to a plane by the stereographic proj
ection."}}{SEP_R 9 0}{INP_R 10 0 "> "{TEXT 0 47 "p1:=cos(v)*cos(u
):p2:=cos(v)*sin(u):p3:=sin(v):"}}{SEP_R 11 0}{INP_R 12 0 "> "
{TEXT 0 188 "animate3d(\012[(1-t)*p1+t*p1/(1-p3),(1-t)*p2+t*p2/(1
-p3),(1-t)*p3],\012u=0..2*Pi,v=-Pi/2..1,t=0..1,\012scaling=constr
ained,style=patch,color=sin(v),\012title=`Animating the Stereogra
phic Projection`);"}}{SEP_R 13 0}{COM_R 14 0{TEXT 1 29 "Degree tw
o map of the sphere."}}{SEP_R 15 0}{INP_R 16 0 "> "{TEXT 0 96 "sq
1:=animate3d(\012[cos(v)*cos(t*u),cos(v)*sin(t*u),sin(v)],\012u=0
..Pi,v=-Pi/2..Pi/2,t=1..2,color=u):"}}{SEP_R 17 0}{INP_R 18 0 "> \+
"{TEXT 0 101 "sq2:=animate3d(\012[3+cos(v)*cos(t*u),cos(v)*sin(t*
u),sin(v)],\012u=Pi..2*Pi,v=-Pi/2..Pi/2,t=1..2,color=u):"}}{SEP_R
 19 0}{INP_R 20 0 "> "{TEXT 0 164 "display([sq1,sq2],insequence=f
alse,\012style=patchnogrid,scaling=constrained,orientation=[-34,4
8],\012titlefont=[TIMES,ROMAN,18],title=`Degree two map of  the s
phere I`);"}}{SEP_R 21 0}{INP_R 22 0 "> "{TEXT 0 149 "belt:=anima
te3d(\012[(1+0.05*(t-1)*u)*cos(v)*cos(t*u),(1+0.05*(t-1)*u)*cos(v
)*sin(t*u),sin(v)],\012u=0..1.98*Pi,v=-Pi/8..Pi/8,t=1..2,grid=[60
,12],color=u):"}}{SEP_R 23 0}{INP_R 24 0 "> "{TEXT 0 229 "cups:=a
nimate3d(\{\012[(1+0.05*(t-1)*u)*cos(v)*cos(t*u),(1+0.05*(t-1)*u)
*cos(v)*sin(t*u),sin(v)],\012[(1+0.05*(t-1)*u)*cos(v)*cos(t*u),(1
+0.05*(t-1)*u)*cos(v)*sin(t*u),-sin(v)]\012\},\012u=0..1.98*Pi,v=
Pi/4..Pi/2,t=1..2,\012grid=[60,12],color=u):"}}{SEP_R 25 0}{INP_R
 26 0 "> "{TEXT 0 199 "display3d(\{belt,cups\},\012shading=zhue,s
tyle=patchcontour,contours=8,thickness=3,\012scaling=constrained,
orientation=[-38,76],frames=10,\012titlefont=[TIMES,ROMAN,18],tit
le=`Degree two map of the sphere II`);"}}{SEP_R 27 0}{COM_R 28 0
{TEXT 1 71 "The torus is obtained from a rectangle by side pairin
g transformations."}}{SEP_R 29 0}{INP_R 30 0 "> "{TEXT 0 127 "A:=
animate3d(\012[(1-t)*x+t*exp(x)*cos(y),(1-t)*y+t*exp(x)*sin(y),0]
,\012x=Pi/4..Pi/2,y=0..Pi,t=0..1,color=x,frames=10,grid=[15,40]):
"}}{SEP_R 31 0}{INP_R 32 0 "> "{TEXT 0 54 "R:=(exp(Pi/2)+exp(Pi/4
))/2:r:=(exp(Pi/2)-exp(Pi/4))/2:"}}{SEP_R 33 0}{INP_R 34 0 "> "
{TEXT 0 248 "B:=animate3d(\012[(R+(4*r/Pi)*sin((Pi/(4*r))*t*(exp(
x)-R))/t)*cos((1+t/4)*y),\012(R+(4*r/Pi)*sin((Pi/(4*r))*t*(exp(x)
-R))/t)*sin((1+t/4)*y),\012((4*r)/Pi)*(1-cos((Pi/(4*r))*t*(exp(x)
-R)))/t],\012x=Pi/4..Pi/2,y=0..Pi,t=-0.005..4,color=x,frames=10,g
rid=[15,40]):"}}{SEP_R 35 0}{INP_R 36 0 "> "{TEXT 0 168 "display(
[A,B],insequence=true,\012style=patchnogrid,thickness=2,scaling=c
onstrained,orientation=[-24,64],\012title=`The Torus is a Rectang
le with Opposite Sides Identified`);"}}{SEP_R 37 0}{COM_R 38 0
{TEXT 1 61 "The Klein Bottle is traced by a figure eight moving i
n space."}}{SEP_R 39 0}{INP_R 40 0 "> "{TEXT 0 306 "animate3d(\01
2[(2+cos(t*u/2)*sin(v)-sin(t*u/2)*sin(2*v))*cos(t*u),\012(2+cos(t
*u/2)*sin(v)-sin(t*u/2)*sin(2*v))*sin(t*u),\012sin(t*u/2)*sin(v)+
cos(t*u/2)*sin(2*v)],\012u=0..2*Pi,v=0..2*Pi,t=0..1,grid=[30,40],
orientation=[-40,53],scaling=constrained,\012style=patchnogrid,co
lor=sin(v),\012title=`Animating the Klein Bottle`);"}}{SEP_R 41 0
}{COM_R 42 0{TEXT 1 66 "Half of the Klein Bottle is traced by a f
igure S  moving in space."}}{SEP_R 43 0}{INP_R 44 0 "> "{TEXT 0 
319 "animate3d(\012[(2+cos(t*u/2)*sin(v)-sin(t*u/2)*sin(2*v))*cos
(t*u),\012(2+cos(t*u/2)*sin(v)-sin(t*u/2)*sin(2*v))*sin(t*u),\012
sin(t*u/2)*sin(v)+cos(t*u/2)*sin(2*v)],\012u=0..2*Pi,v=-Pi/2..Pi/
2,t=0..1,\012grid=[30,20],orientation=[-40,53],scaling=constraine
d,style=patchnogrid,\012color=sin(v),\012title=`Animating Half of
 the Klein Bottle`);"}}{SEP_R 45 0}{COM_R 46 0{TEXT 1 48 "Two Mob
ius strips join to form the Klein bottle."}}{SEP_R 47 0}{INP_R 48
 0 "> "{TEXT 0 220 "paste1:=animate3d(\012[(2+cos(u/2)*sin(t*v)-s
in(u/2)*sin(2*t*v))*cos(u),\012(2+cos(u/2)*sin(t*v)-sin(u/2)*sin(
2*t*v))*sin(u),\012sin(u/2)*sin(t*v)+cos(u/2)*sin(2*t*v)],\012u=0
..2*Pi,v=-Pi/2..Pi/2,t=1/4..1,grid=[30,15],color=sin(v)):"}}
{SEP_R 49 0}{INP_R 50 0 "> "{TEXT 0 250 "paste2:=animate3d(\012[(
2+cos(u/2)*sin(t*v+Pi)-sin(u/2)*sin(2*(t*v+Pi)))*cos(u),\012(2+co
s(u/2)*sin(t*v+Pi)-sin(u/2)*sin(2*(t*v+Pi)))*sin(u),\012sin(u/2)*
sin(t*v+Pi)+cos(u/2)*sin(2*(t*v+Pi))+5-5*t],\012u=0..2*Pi,v=-Pi/2
..Pi/2,t=1/4..1,grid=[30,15],color=sin(v)):"}}{SEP_R 51 0}{INP_R 
52 0 "> "{TEXT 0 98 "display3d([paste1,paste2],\012style=patchnog
rid,scaling=constrained,shading=Z,orientation=[-104,71]);"}}}{END
}