The Mathematical Madness of Möbius Strips and Other One-Sided Objects
Möbius Born, His Strip Soon Discovered | History Channel on Foxtel
It can be realized as a ruled surface. Its boundary is a simple closed curve, that is, homeomorphic to a circle. Some of these can be smoothly modeled in Euclidean space , and others cannot. In particular, the twisted paper model is a developable surface , having zero Gaussian curvature. A system of differential-algebraic equations that describes models of this type was published in together with its numerical solution.
Like the cylinder , it is not a true surface, but rather a surface with boundary Henle , p. According to Madachy , the B. Trott, pers.
Try to draw a line on both "sides" without picking up your pencil. It's actually quite simple. That is, when we define a surface normal at a point, it is impossible to extend the definition to the whole surface. The picture below illustrates that by "sliding" a given surface normal along the strip, without picking it up, we can get a surface normal that points in the opposite direction. Thus any attempt to give the surface a "front" and a "back" must fail.