IX

> restart;
> r:=sqrt(24)/3;
> with(plots):
> 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/3):
> q23:=expand((1-u)*q2+u*q3):
> p23:=plot3d(q23,u=0..1,t=0..2*Pi/3):
> q34:=expand((1-u)*q3+u*q4):
> p34:=plot3d(q34,u=0..1,t=0..2*Pi/3):
> display(p12,p23,p34);

> restart;
> r:=sqrt(24)/3;
> with(plots):
> 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):
> q23:=expand((1-u)*q2+u*q3):
> p23:=plot3d(q23,u=0..1,t=0..2*Pi):
> q34:=expand((1-u)*q3+u*q4):
> p34:=plot3d(q34,u=0..1,t=0..2*Pi):
> display(p12,p23,p34);

> restart;
> r:=sqrt(24)/3;
> with(plots):
> 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);
> restart;
> with(plots):
> p1:=plot3d([1,theta,phi],theta=0..Pi,phi=0..2*Pi/3,coords=spherical):
> phi:=2*Pi/3;rho:=1;
> z:=rho*cos(phi);
> r:=rho*sin(phi);
> x:=r*cos(theta);
> y:=r*sin(theta);
> [x,y,z];
> q:=expand((1-u)*[0,0,-2]+u*[x,y,z]);
> p2:=plot3d(q,u=0..1,theta=0..Pi):
> display(p1,p2,scaling=constrained);

> restart;
> with(plots):with(plottools):
> p1:=display(sphere([0,0,1],1)):
> p2:=display(sphere([1,1,0.3],0.3)):
> p3:=display(sphere([0,2,0.5],0.5)):
> display(p1,p2,p3,scaling=constrained);
> 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=4):
> expand(u2*[0,0,1]+(1-u2)*[1,1,0.3]);
> u2:=-3/7;
> expand(u2*[0,0,1]+(1-u2)*[1,1,0.3]);
> p12:=display(line([10/7,10/7,0],[0,0,0]),thickness=3):
> pp:=display(p12,p23,p31):
> ppp:=reflect(pp,[[0,0,1],[1,1,0.3],[0,2,0.5]]):
> pppp:=line([0,4,0],[5/2,-1/2,0]):
> display(p1,p2,p3,pp,ppp,pppp,scaling=constrained);

> restart;
> q:=expand((1-v)*[cos(t),0,1]+v*[0,sin(t),-1]);
> plot3d(q,v=0..1,t=0..2*Pi,scaling=constrained);
¡@

> restart;
> m:=[[x,0],[0,y]];
> x:=cos(t);
> y:=sin(t);
> t:=n*2*Pi/100;
> plot([m$n=1..100],scaling=constrained,axes=none);

> restart;
> t:=Pi*n/100;
> x:=cos(t)-1;
> y:=sin(t);
> x1:=sqrt(1-(y-1)^2);
> m:=[[x,y],[x,-y],[x1,-y],[x1,y],[x,y]]:
> plot([m$n=1..50],scaling=constrained,color=blue,axes=none);
¡@