Mobius Band

The Mobius Band is the building block for non-orientable surfaces. It is formed by joining the ends of a rectangle with a twist (180 degrees). Any non-orientable surface contains a Mobius Band, and any surface which contains a Mobius Band is necessarily non-orientable. It is not closed--hence it is not a surface, and it contains one boundary curve. The Mobius Band cannot be embedded in the plane, R^2. This is the usual picture of the Mobius band in R^3. It is formed by joining the ends of a rectangle with one twist of 180 degrees.

Code:

for a=0:112;
for b=0:60;
u=a/2;
w=b/2;
v=w/50-0.3;
X(a+1,b+1)=cos(u)+v*cos(u/2)*cos(u);
Y(a+1,b+1)=sin(u)+v*cos(u/2)*sin(u);
Z(a+1,b+1)=v*sin(u/2);
T(a+1,b+1)=u;
end
end

surf(X,Y,Z,-X)
view(55, 50)
shading interp
light
lighting phong
material dull

set(gcf, 'color', 'w')
colormap hsv