Mathematical Experiment 9

Construct various cross-sections of a cone.

When a cube is rotated about its main diagonal, describe the region wiped out.
Construct one-half of the tangent cone of a sphere.

Construct a surface which appears as a triangle along the x-axis,

appears as a triangle along the y-axis,

 

apprears as an astroid along the z-axis

Construct this pattern form by line segments joining [cos(t),0] with [0,sin(t)] as t ranges over the interval [0,2p].

@

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

Construct this pattern:

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);