http://en.wikipedia.org/wiki/M%C3%B6bius_strip
It is called the Sudanese Mobius Band.
alas, it requires complex numbers.
"To see this, first consider such an embedding into the 3-sphere S3 regarded as a subset of R4. A parametrization for this embedding is given by"
z1 = sin(eta*e^(i*phi))
z2 = cos(eta*e^(i*phi/2)).
and |z1|^2+|z2|^2=1 and "therefore the entire surface lies on S^3"
what does that phrase mean? does this have something do do with the fact that this lies on a circle instead of a flat line strip? it's beginning to look like it. x^2+y^2=r^2 is the equation for a circle, so if r=1...
eta runs from 0 to pi
phi runs 0 to 2pi
They said this is in the complex space C2 instead of R4.
I don't have my math books handy anymore and I'm a little rusty lately, so does anyone know how to put this into Euclidian space (R4)?
It will be interesting to try to decide where to draw lines to and from...
public class z{public z(){System.out.println("Hi");} public static void main(String[] args){z p=new z();}}
Jim Michaels