# Klein bagel ( "figure 8" immersion x-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.

## Variables

x | X-coordinate (dimensionless) |

θ | The angle in the xy-plane ( 0 ≤ θ < 2π ) (dimensionless) |

r | The radius of the circle (dimensionless) |

v | The angle that specifies the position around the 8-shaped cross section ( 0 ≤ v < 2π) (dimensionless) |