with(plots):with(plottools):
r:=sqrt(24)/3;
q1:=[0,0,sqrt(3)]:
x:=r*cos(t);y:=r*sin(t);z:=sqrt(3)/3;
q2:=[x,y,z];
p:=Pi/3;
x1:=r*cos(t+p);y1:=r*sin(t+p);
z1:=-sqrt(3)/3;
q3:=[x1,y1,z1];
q4:=[0,0,-sqrt(3)];
q12:=expand((1-u)*q1+u*q2):
p12:=plot3d(q12,u=0..1,t=0..2*Pi,color=red):
q23:=expand((1-u)*q2+u*q3):
p23:=plot3d(q23,u=0..1,t=0..2*Pi,color=green):
q34:=expand((1-u)*q3+u*q4):
p34:=plot3d(q34,u=0..1,t=0..2*Pi,color=blue):
with(plots):with(plottools):
r:=sqrt(24)/3;
q1:=[0,0,sqrt(3)]:
x:=r*cos(t);y:=r*sin(t);z:=sqrt(3)/3;
q2:=[x,y,z];
p:=Pi/3;
x1:=r*cos(t+p);y1:=r*sin(t+p);z1:=-sqrt(3)/3;
q3:=[x1,y1,z1];
q4:=[0,0,-sqrt(3)];
q12:=expand((1-u)*q1+u*q2):
q23:=expand((1-u)*q2+u*q3):
q34:=expand((1-u)*q3+u*q4):
s12:=plot3d(q12,u=0..1,t=0..2*Pi/3,color=red):
s23:=plot3d(q23,u=0..1,t=0..2*Pi/3,color=green):
s34:=plot3d(q34,u=0..1,t=0..2*Pi/3,color=blue):
p1:=plot3d([1,theta,phi],theta=0..Pi,
phi=0..2*Pi/3,coords=spherical,
scaling=constrained):
phi:=2*Pi/3;rho:=1;
z:=rho*cos(phi);
r:=rho*sin(phi);
x:=r*cos(theta);y:=r*sin(theta);
q:=expand((1-u)*[0,0,-2]+u*[x,y,z]);
p2:=plot3d(q,u=0..1,theta=0..Pi,scaling=constrained):
with(plots):
with(plots):with(plottools):
s1:=display(sphere([0,0,1],1)):
s2:=display(sphere([1,1,0.3],0.3)):
s3:=display(sphere([0,2,0.5],0.5)):
expand((1-u)*[1,1,0.3]+u*[0,2,0.5]);
u:=-3/2;
expand((1-u)*[1,1,0.3]+u*[0,2,0.5]);
p23:=display(line([0,2,0],[5/2,
-1/2, 0]),thickness=3):
expand((1-u1)*[0,2,0.5]+u1*[0,0,1]);
u1:=-1;
expand((1-u1)*[0,2,0.5]+u1*[0,0,1]);
p31:=display(line([0, 4,
0.],[0,0,0]),thickness=3):
expand((1-u2)*[1,1,0.3]+u2*[0,0,1]);
u2:=-3/7;
expand((1-u2)*[1,1,0.3]+u2*[0,0,1]);
p12:=display(line([10/7, 10/7,
0.],[0,0,0]),thickness=3):
pp:=display(p12,p31,p23):
qq:=reflect(pp,[[0,0,1],[1,1,0.3],[0,2,0.5]]):
pppp:=line([0,4,0],[5/2,-1/2,0]):
display(s1,s2,s3,p12,p23,p31,pp,qq,pppp,scaling=constrained);
q:=expand((1-v)*[cos(t),0,1]+v*[0,sin(t),-1]):
scaling=constrained,color=pink);
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m:=[[cos(t),0],[0,sin(t)]]:t:=n*2*Pi/100; plot([m$n=1..100]color=cyan,scaling=constrained, axes=none);
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t:=n*Pi/100; x:=cos(t)-1;y:=sin(t); x1:=sqrt(1-(1-y)^2); m:=[[x,y],[x,-y],[x1,-y],[x1,y],[x,y]]: color=blue,axes=none);
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