已知平行截面面积求立体的体积图形动画计算.pptx

http:/ July 1,2012四川大学数学学院 徐小湛切片法 1用数学软件用数学软件Maple作了有关动画作了有关动画这些动画生动地显示了立体的形成过程这些动画生动地显示了立体的形成过程计算了一些立体的体积计算了一些立体的体积http:/ July 1,2012四川大学数学学院 徐小湛切片法 2http:/ July 1,2012四川大学数学学院 徐小湛切片法 3with(plots):f:=x-x2/10+1:g:=x-x4/150-1:a:=-3:b:=3:H:=3:xzou:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):yzou:=spacecurve(0,y,0,y=a-1.b+1,thickness=3,color=black):base:=plot3d(x,y,0,x=a.b,y=g(x).f(x),color=grey,style=patchnogrid):quxianf:=spacecurve(x,f(x),0,x=a-1.b+1,thickness=3,color=red):quxiang:=spacecurve(x,g(x),0,x=a-1.b+1,thickness=3,color=red):K:=50:for i from 0 to K do xi:=a+i*(b-a)/K:sanjiaoxingi:=spacecurve(xi,g(xi),0,xi,f(xi),0,xi,(f(xi)+g(xi)/2,H,xi,g(xi),0,thickness=3,color=blue):sanjiaobani:=plot3d(xi,y,z,y=(f(xi)+g(xi)/2-(f(xi)-g(xi)/2*(1-z/H).(f(xi)+g(xi)/2+(f(xi)-g(xi)/2*(1-z/H),z=0.H,color=yellow,style=patchnogrid):qumian1i:=plot3d(x,f(x)+(-f(x)+g(x)/2*t,H*t,t=0.1,x=a.xi,color=green):qumian2i:=plot3d(x,g(x)+(f(x)-g(x)/2*t,H*t,t=0.1,x=a.xi,color=green)od:sanjiaoxing:=display(seq(sanjiaoxingi,i=0.K),insequence=true):sanjiaoban:=display(seq(sanjiaobani,i=0.K),insequence=true):qumian1:=display(seq(qumian1i,i=0.K),insequence=true):qumian2:=display(seq(qumian2i,i=0.K),insequence=true):display(xzou,yzou,base,quxianf,quxiang,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=constrained);动画的Maple程序http:/ July 1,2012四川大学数学学院 徐小湛切片法 4f:=x-(3/2)*(x2/10+x4/150+2):a:=-3:b:=3:Integrate(f(x),x=a.b)=integrate(f(x),x=a.b);现在来求这个立体的体积现在来求这个立体的体积http:/ July 1,2012四川大学数学学院 徐小湛切片法 5这个立体叫做这个立体叫做正劈锥体正劈锥体http:/ July 1,2012四川大学数学学院 徐小湛切片法 6with(plots):R:=1:f:=x-sqrt(R2-x2):g:=x-sqrt(R2-x2):a:=-R:b:=R:H:=2:xzou:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):yzou:=spacecurve(0,y,0,y=a-1.b+1,thickness=3,color=black):base:=plot3d(x,y,0,x=a.b,y=g(x).f(x),color=grey,style=patchnogrid):quxian:=spacecurve(R*cos(t),R*sin(t),0,t=0.2*Pi,thickness=3,color=red):K:=60:for i from 0 to K do xi:=a+i*(b-a)/K:sanjiaoxingi:=spacecurve(xi,g(xi),0,xi,f(xi),0,xi,(f(xi)+g(xi)/2,H,xi,g(xi),0,thickness=3,color=blue):sanjiaobani:=plot3d(xi,y,z,y=(f(xi)+g(xi)/2-(f(xi)-g(xi)/2*(1-z/H).(f(xi)+g(xi)/2+(f(xi)-g(xi)/2*(1-z/H),z=0.H,color=yellow,style=patchnogrid):qumian1i:=plot3d(x,f(x)+(-f(x)+g(x)/2*t,H*t,t=0.1,x=a.xi,color=green):qumian2i:=plot3d(x,g(x)+(f(x)-g(x)/2*t,H*t,t=0.1,x=a.xi,color=green)od:sanjiaoxing:=display(seq(sanjiaoxingi,i=0.K),insequence=true):sanjiaoban:=display(seq(sanjiaobani,i=0.K),insequence=true):qumian1:=display(seq(qumian1i,i=0.K),insequence=true):qumian2:=display(seq(qumian2i,i=0.K),insequence=true):display(xzou,yzou,base,quxian,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=constrained,orientation=-50,70);动画的Maple程序http:/ July 1,2012四川大学数学学院 徐小湛切片法 7with(plots):R:=1:f:=x-sqrt(R2-x2):g:=x-sqrt(R2-x2):a:=-R:b:=R:H:=2:xzou:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):yzou:=spacecurve(0,y,0,y=a-1.b+1,thickness=3,color=black):base:=plot3d(x,y,0,x=a.b,y=g(x).f(x),color=grey,style=patchnogrid):quxian:=spacecurve(R*cos(t),R*sin(t),0,t=0.2*Pi,thickness=3,color=red):xi:=0.5*R:sanjiaoxing:=spacecurve(xi,g(xi),0,xi,f(xi),0,xi,(f(xi)+g(xi)/2,H,xi,g(xi),0,thickness=3,color=blue):sanjiaoban:=plot3d(xi,y,z,y=(f(xi)+g(xi)/2-(f(xi)-g(xi)/2*(1-z/H).(f(xi)+g(xi)/2+(f(xi)-g(xi)/2*(1-z/H),z=0.H,color=yellow,style=patchnogrid):qumian1:=plot3d(x,f(x)+(-f(x)+g(x)/2*t,H*t,t=0.1,x=a.xi,color=green):qumian2:=plot3d(x,g(x)+(f(x)-g(x)/2*t,H*t,t=0.1,x=a.xi,color=green):display(xzou,yzou,base,quxian,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=constrained,orientation=-50,70);http:/ July 1,2012四川大学数学学院 徐小湛切片法 8with(plots):R:=1.7:f:=x-sqrt(R2-x2):g:=x-sqrt(R2-x2):a:=-R:b:=R:H:=3:xzou:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):yzou:=spacecurve(0,y,0,y=a-1.b+1,thickness=3,color=black):base:=plot3d(x,y,0,x=a.b,y=g(x).f(x),color=grey,style=patchnogrid):quxian:=spacecurve(R*cos(t),R*sin(t),0,t=0.2*Pi,thickness=3,color=red):K:=8:for i from 0 to K do xi:=a+i*(b-a)/K:sanjiaoxingi:=spacecurve(xi,g(xi),0,xi,f(xi),0,xi,(f(xi)+g(xi)/2,H,xi,g(xi),0,thickness=3,color=blue):sanjiaobani:=plot3d(xi,y,z,y=(f(xi)+g(xi)/2-(f(xi)-g(xi)/2*(1-z/H).(f(xi)+g(xi)/2+(f(xi)-g(xi)/2*(1-z/H),z=0.H,color=yellow,style=patchnogrid):od:sanjiaoxing:=display(seq(sanjiaoxingi,i=0.K),insequence=false):sanjiaoban:=display(seq(sanjiaobani,i=0.K),insequence=false):qumian1:=plot3d(x,f(x)+(-f(x)+g(x)/2*t,H*t,t=0.1,x=a.b,color=green,style=wireframe,grid=50,30):qumian2:=plot3d(x,g(x)+(f(x)-g(x)/2*t,H*t,t=0.1,x=a.b,color=green,style=wireframe,grid=50,30):display(xzou,yzou,base,quxian,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=constrained,orientation=-50,70);http:/ July 1,2012四川大学数学学院 徐小湛切片法 9见同济见同济高等数学高等数学6版，版，281页，例页，例10现在来求这个现在来求这个立体的体积立体的体积http:/ July 1,2012四川大学数学学院 徐小湛切片法 10http:/ July 1,2012四川大学数学学院 徐小湛切片法 11with(plots):f:=x-sin(x/2)+2:g:=x-cos(x/3)-2:a:=-Pi:b:=Pi:xzou:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):yzou:=spacecurve(0,y,0,y=a-1.b+1,thickness=3,color=black):base:=plot3d(x,y,0,x=a.b,y=g(x).f(x),color=grey,style=patchnogrid):quxianf:=spacecurve(x,f(x),0,x=a-1.b+1,thickness=3,color=red):quxiang:=spacecurve(x,g(x),0,x=a-1.b+1,thickness=3,color=red):K:=60:for i from 0 to K do xi:=a+i*(b-a)/K:sanjiaoxingi:=spacecurve(xi,g(xi),0,xi,f(xi),0,xi,(f(xi)+g(xi)/2,sqrt(3)/2*(f(xi)-g(xi),xi,g(xi),0,thickness=3,color=blue):sanjiaobani:=plot3d(xi,y,z,y=(f(xi)+g(xi)/2-(f(xi)-g(xi)/2+z/sqrt(3).(f(xi)+g(xi)/2+(f(xi)-g(xi)/2-z/sqrt(3),z=0.sqrt(3)/2*(f(xi)-g(xi),color=yellow,style=patchnogrid):qumian1i:=plot3d(x,f(x)+(-f(x)+g(x)/2*t,(sqrt(3)/2)*(f(x)-g(x)*t,t=0.1,x=a.xi,color=green):qumian2i:=plot3d(x,g(x)+(f(x)-g(x)/2*t,(sqrt(3)/2)*(f(x)-g(x)*t,t=0.1,x=a.xi,color=green)od:sanjiaoxing:=display(seq(sanjiaoxingi,i=0.K),insequence=true):sanjiaoban:=display(seq(sanjiaobani,i=0.K),insequence=true):qumian1:=display(seq(qumian1i,i=0.K),insequence=true):qumian2:=display(seq(qumian2i,i=0.K),insequence=true):display(xzou,yzou,base,quxianf,quxiang,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=constrained);动画的Maple程序http:/ July 1,2012四川大学数学学院 徐小湛切片法 12f:=x-(sqrt(3)/4)*(sin(x/2)-cos(x/3)+4)2:a:=-Pi:b:=Pi:Integrate(f(x),x=a.b)=integrate(f(x),x=a.b);evalf(%);现在来求这个立体的体积现在来求这个立体的体积http:/ July 1,2012四川大学数学学院 徐小湛切片法 13http:/ July 1,2012四川大学数学学院 徐小湛切片法 14R:=1.6:f:=x-sqrt(R2-x2):g:=x-sqrt(R2-x2):a:=-R:b:=R:H:=2:xzou:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):yzou:=spacecurve(0,y,0,y=a-1.b+1,thickness=3,color=black):base:=plot3d(x,y,0,x=a.b,y=g(x).f(x),color=grey,style=patchnogrid):quxian:=spacecurve(R*cos(t),R*sin(t),0,t=0.2*Pi,thickness=3,color=red):K:=60:for i from 0 to K do xi:=a+i*(b-a)/K:sanjiaoxingi:=spacecurve(xi,g(xi),0,xi,f(xi),0,xi,(f(xi)+g(xi)/2,sqrt(3)/2*(f(xi)-g(xi),xi,g(xi),0,thickness=3,color=blue):sanjiaobani:=plot3d(xi,y,z,y=(f(xi)+g(xi)/2-(f(xi)-g(xi)/2+z/sqrt(3).(f(xi)+g(xi)/2+(f(xi)-g(xi)/2-z/sqrt(3),z=0.sqrt(3)/2*(f(xi)-g(xi),color=yellow,style=patchnogrid):qumian1i:=plot3d(x,f(x)+(-f(x)+g(x)/2*t,(sqrt(3)/2)*(f(x)-g(x)*t,t=0.1,x=a.xi,color=green):qumian2i:=plot3d(x,g(x)+(f(x)-g(x)/2*t,(sqrt(3)/2)*(f(x)-g(x)*t,t=0.1,x=a.xi,color=green)od:sanjiaoxing:=display(seq(sanjiaoxingi,i=0.K),insequence=true):sanjiaoban:=display(seq(sanjiaobani,i=0.K),insequence=true):qumian1:=display(seq(qumian1i,i=0.K),insequence=true):qumian2:=display(seq(qumian2i,i=0.K),insequence=true):display(xzou,yzou,base,quxian,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=constrained,orientation=-50,70);动画的Maple程序http:/ July 1,2012四川大学数学学院 徐小湛切片法 15R:=1.6:f:=x-sqrt(R2-x2):g:=x-sqrt(R2-x2):a:=-R:b:=R:H:=2:xzou:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):yzou:=spacecurve(0,y,0,y=a-1.b+1,thickness=3,color=black):base:=plot3d(x,y,0,x=a.b,y=g(x).f(x),color=grey,style=patchnogrid):quxian:=spacecurve(R*cos(t),R*sin(t),0,t=0.2*Pi,thickness=3,color=red):xi:=0.2*R:sanjiaoxing:=spacecurve(xi,g(xi),0,xi,f(xi),0,xi,(f(xi)+g(xi)/2,sqrt(3)/2*(f(xi)-g(xi),xi,g(xi),0,thickness=3,color=blue):sanjiaoban:=plot3d(xi,y,z,y=(f(xi)+g(xi)/2-(f(xi)-g(xi)/2+z/sqrt(3).(f(xi)+g(xi)/2+(f(xi)-g(xi)/2-z/sqrt(3),z=0.sqrt(3)/2*(f(xi)-g(xi),color=yellow,style=patchnogrid):qumian1:=plot3d(x,f(x)+(-f(x)+g(x)/2*t,(sqrt(3)/2)*(f(x)-g(x)*t,t=0.1,x=a.xi,color=green):qumian2:=plot3d(x,g(x)+(f(x)-g(x)/2*t,(sqrt(3)/2)*(f(x)-g(x)*t,t=0.1,x=a.xi,color=green):display(xzou,yzou,base,quxian,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=constrained,orientation=-50,70);http:/ July 1,2012四川大学数学学院 徐小湛切片法 16R:=1.6:f:=x-sqrt(R2-x2):g:=x-sqrt(R2-x2):a:=-R:b:=R:H:=2:xzou:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):yzou:=spacecurve(0,y,0,y=a-1.b+1,thickness=3,color=black):base:=plot3d(x,y,0,x=a.b,y=g(x).f(x),color=grey,style=patchnogrid):quxian:=spacecurve(R*cos(t),R*sin(t),0,t=0.2*Pi,thickness=3,color=red):K:=8:for i from 0 to K do xi:=a+i*(b-a)/K:sanjiaoxingi:=spacecurve(xi,g(xi),0,xi,f(xi),0,xi,(f(xi)+g(xi)/2,sqrt(3)/2*(f(xi)-g(xi),xi,g(xi),0,thickness=3,color=blue):sanjiaobani:=plot3d(xi,y,z,y=(f(xi)+g(xi)/2-(f(xi)-g(xi)/2+z/sqrt(3).(f(xi)+g(xi)/2+(f(xi)-g(xi)/2-z/sqrt(3),z=0.sqrt(3)/2*(f(xi)-g(xi),color=yellow,style=patchnogrid)od:sanjiaoxing:=display(seq(sanjiaoxingi,i=0.K),insequence=false):sanjiaoban:=display(seq(sanjiaobani,i=0.K),insequence=false):qumian1:=plot3d(x,f(x)+(-f(x)+g(x)/2*t,(sqrt(3)/2)*(f(x)-g(x)*t,t=0.1,x=a.b,style=wireframe):qumian2:=plot3d(x,g(x)+(f(x)-g(x)/2*t,(sqrt(3)/2)*(f(x)-g(x)*t,t=0.1,x=a.b,style=wireframe):display(xzou,yzou,base,quxian,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=constrained,orientation=-50,70);http:/ July 1,2012四川大学数学学院 徐小湛切片法 17见同济见同济高等数学高等数学6版，版，286页，页，18题题现在来求这个现在来求这个立体的体积立体的体积http:/ July 1,2012四川大学数学学院 徐小湛切片法 18http:/ July 1,2012四川大学数学学院 徐小湛切片法 19with(plots):f:=x-sin(x)+1:g:=x-sin(x-1)-1:a:=-Pi:b:=2*Pi:xzou:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):yzou:=spacecurve(0,y,0,y=a-1.b+1,thickness=3,color=black):base:=plot3d(x,y,0,x=a.b,y=g(x).f(x),color=grey,style=patchnogrid):quxianf:=spacecurve(x,f(x),0,x=a-1.b+1,thickness=3,color=red):quxiang:=spacecurve(x,g(x),0,x=a-1.b+1,thickness=3,color=red):K:=60:for i from 0 to K do xi:=a+i*(b-a)/K:zhengfangxingi:=spacecurve(xi,g(xi),0,xi,f(xi),0,xi,f(xi),f(xi)-g(xi),xi,g(xi),f(xi)-g(xi),xi,g(xi),0,thickness=3,color=blue):zhengfangbani:=plot3d(xi,y,z,y=g(xi).f(xi),z=0.f(xi)-g(xi),color=yellow,style=patchnogrid):qumian1i:=plot3d(x,f(x),(f(x)-g(x)*t,t=0.1,x=a.xi,color=green):qumian2i:=plot3d(x,g(x),(f(x)-g(x)*t,t=0.1,x=a.xi,color=green):qumian3i:=plot3d(x,g(x)+(f(x)-g(x)*t,f(x)-g(x),t=0.1,x=a.xi,color=green)od:zhengfangxing:=display(seq(zhengfangxingi,i=0.K),insequence=true):zhengfangban:=display(seq(zhengfangbani,i=0.K),insequence=true):qumian1:=display(seq(qumian1i,i=0.K),insequence=true):qumian2:=display(seq(qumian2i,i=0.K),insequence=true):qumian3:=display(seq(qumian3i,i=0.K),insequence=true):display(xzou,yzou,base,quxianf,quxiang,zhengfangban,zhengfangxing,qumian1,qumian2,qumian3,scaling=constrained);动画的Maple程序http:/ July 1,2012四川大学数学学院 徐小湛切片法 20http:/ July 1,2012四川大学数学学院 徐小湛切片法 21http:/ July 1,2012四川大学数学学院 徐小湛切片法 22http:/ July 1,2012四川大学数学学院 徐小湛切片法 23with(plots):R:=1.6:f:=x-sqrt(R2-x2):g:=x-sqrt(R2-x2):a:=-R:b:=R:H:=2:xzou:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):yzou:=spacecurve(0,y,0,y=a-1.b+1,thickness=3,color=black):base:=plot3d(x,y,0,x=a.b,y=g(x).f(x),color=grey,style=patchnogrid):quxian:=spacecurve(R*cos(t),R*sin(t),0,t=0.2*Pi,thickness=3,color=red):K:=60:for i from 0 to K do xi:=a+i*(b-a)/K:zhengfangxingi:=spacecurve(xi,g(xi),0,xi,f(xi),0,xi,f(xi),f(xi)-g(xi),xi,g(xi),f(xi)-g(xi),xi,g(xi),0,thickness=3,color=blue):zhengfangbani:=plot3d(xi,y,z,y=g(xi).f(xi),z=0.f(xi)-g(xi),color=yellow,style=patchnogrid):qumian1i:=plot3d(x,f(x),(f(x)-g(x)*t,t=0.1,x=a.xi,color=green):qumian2i:=plot3d(x,g(x),(f(x)-g(x)*t,t=0.1,x=a.xi,color=green):qumian3i:=plot3d(x,g(x)+(f(x)-g(x)*t,f(x)-g(x),t=0.1,x=a.xi,color=grey)od:zhengfangxing:=display(seq(zhengfangxingi,i=0.K),insequence=true):zhengfangban:=display(seq(zhengfangbani,i=0.K),insequence=true):qumian1:=display(seq(qumian1i,i=0.K),insequence=true):qumian2:=display(seq(qumian2i,i=0.K),insequence=true):qumian3:=display(seq(qumian3i,i=0.K),insequence=true):display(xzou,yzou,base,quxian,zhengfangban,zhengfangxing,qumian1,qumian2,qumian3,scaling=constrained,orientation=-60,70);动画的Maple程序http:/ July 1,2012四川大学数学学院 徐小湛切片法 24这个体积刚好等于这个体积刚好等于牟合方盖牟合方盖的体积的体积见同济见同济高等数学高等数学6版，下册版，下册143页，例页，例4现在来求这个现在来求这个立体的体积立体的体积http:/ July 1,2012四川大学数学学院 徐小湛切片法 25http:/ July 1,2012四川大学数学学院 徐小湛切片法 26with(plots):f:=x-sin(x)+2:g:=x-sin(x-1)-1:a:=-Pi:b:=2*Pi:xzou:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):yzou:=spacecurve(0,y,0,y=-2.3,thickness=3,color=black):base:=plot3d(x,y,0,x=a.b,y=g(x).f(x),color=grey,style=patchnogrid):quxianf:=spacecurve(x,f(x),0,x=a-1.b+1,thickness=3,color=red):quxiang:=spacecurve(x,g(x),0,x=a-1.b+1,thickness=3,color=red):K:=60:for i from 0 to K do xi:=a+i*(b-a)/K:banyuani:=spacecurve(xi,(f(xi)+g(xi)/2+(f(xi)-g(xi)/2*cos(t),(f(xi)-g(xi)/2*sin(t),t=0.Pi,thickness=3,color=blue):dixiani:=spacecurve(xi,y,0,y=g(xi).f(xi),thickness=3,color=blue):banyuanbani:=plot3d(xi,(f(xi)+g(xi)/2+r*cos(t),r*sin(t),r=0.(f(xi)-g(xi)/2,t=0.Pi,color=yellow,style=patchnogrid):qumiani:=plot3d(x,(f(x)+g(x)/2+(f(x)-g(x)/2*cos(t),(f(x)-g(x)/2*sin(t),t=0.Pi,x=a.xi,color=green)od:banyuan:=display(seq(banyuani,i=0.K),insequence=true):dixian:=display(seq(dixiani,i=0.K),insequence=true):banyuanban:=display(seq(banyuanbani,i=0.K),insequence=true):qumian:=display(seq(qumiani,i=0.K),insequence=true):display(xzou,yzou,quxianf,quxiang,banyuanban,base,banyuan,qumian,dixian,scaling=constrained);动画的Maple程序http:/ July 1,2012四川大学数学学院 徐小湛切片法 27http:/ July 1,2012四川大学数学学院 徐小湛切片法 28with(plots):f:=x-sin(x)+2:g:=x-sin(x-1)-1:a:=-Pi:b:=2*Pi:xzou:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):yzou:=spacecurve(0,y,0,y=-2.3,thickness=3,color=black):quxianf:=spacecurve(x,f(x),0,x=a-1.b+1,thickness=3,color=red):quxiang:=spacecurve(x,g(x),0,x=a-1.b+1,thickness=3,color=red):K:=60:for i from 0 to K do xi:=a+i*(b-a)/K:banyuani:=spacecurve(xi,(f(xi)+g(xi)/2+(f(xi)-g(xi)/2*cos(t),(f(xi)-g(xi)/2*sin(t),t=0.Pi,thickness=3,color=blue):dixiani:=spacecurve(xi,y,0,y=g(xi).f(xi),thickness=3,color=blue):banyuanbani:=plot3d(xi,(f(xi)+g(xi)/2+r*cos(t),r*sin(t),r=0.(f(xi)-g(xi)/2,t=0.Pi,color=yellow,style=patchnogrid):basei:=plot3d(x,y,0,x=a.xi,y=f(x).g(x),color=gray,style=patchnogrid):qumiani:=plot3d(x,(f(x)+g(x)/2+(f(x)-g(x)/2*cos(t),(f(x)-g(x)/2*sin(t),t=0.Pi,x=a.xi,color=green)od:banyuan:=display(seq(banyuani,i=0.K),insequence=true):dixian:=display(seq(dixiani,i=0.K),insequence=true):base:=display(seq(basei,i=0.K),insequence=true):banyuanban:=display(seq(banyuanbani,i=0.K),insequence=true):qumian:=display(seq(qumiani,i=0.K),insequence=true):display(xzou,yzou,quxianf,quxiang,banyuanban,base,banyuan,qumian,dixian,scaling=constrained);动画的Maple程序http:/ July 1,2012四川大学数学学院 徐小湛切片法 29http:/ July 1,2012四川大学数学学院 徐小湛切片法 30with(plots):A:=2:B:=1:a:=-A:b:=A:f:=x-(B/A)*sqrt(A2-x2):g:=x-(B/A)*sqrt(A2-x2):xzou:=spacecurve(x,0,0,x=-A-.5.A+.5,thickness=3,color=black):yzou:=spacecurve(0,y,0,y=-B-.5.B+.5,thickness=3,color=black):base:=plot3d(x,y,0,x=a.b,y=g(x).