Klein bagel ( "figure 8" immersion y-coordinate)

Description

In mathematics, the Klein bottle is an example of a non-orientable surface, informally, it is a surface (a two-dimensional manifold) in which notions of left and right cannot be consistently defined. A Klein bottle has no boundary. The “figure 8” immersion (Klein bagel) of the Klein bottle has a particularly simple parametrization. It is that of a “figure-8” torus with a 180 degree “Möbius” twist inserted. In this immersion, the self-intersection circle (when v = 0, π) is a geometric circle in the xy-plane.

Related formulas

Variables

yY-Coordinate (dimensionless)
θThe angle in the xy-plane ( 0 ≤ θ < 2π ) (dimensionless)
rThe radius of the circle in the xy-plane (dimensionless)
vThe angle that specifies the position around the 8-shaped cross section ( 0 ≤ v < 2π) (dimensionless)