August Ferdinand Möbius (November 17, 1790 – September 26, 1868) was a German mathematician and theoretical astronomer.
He is best known for his discovery of the Möbius strip, a non-orientable two-dimensional surface with only one side when embedded in three-dimensional Euclidean space. It was independently discovered by Johann Benedict Listing around the same time. The Möbius configuration, formed by two mutually inscribed tetrahedra, is also named after him. Möbius was the first to introduce homogeneous coordinates into projective geometry.
The Möbius band (equally known as the Möbius strip) is not a surface of only one geometry (i.e., of only one exact size and shape), such as the half-twisted paper strip depicted in the illustration to the right. Rather, mathematicians refer to the (closed) Möbius band as any surface that is homeomorphic to this strip. Its boundary is a simple closed curve, i.e., homeomorphic to a circle. This allows for a very wide variety of geometric versions of the Möbius band as surfaces each having a definite size and shape. For example, any closed rectangle with length L and width W can be glued to itself (by identifying one edge with the opposite edge after a reversal of orientation) to make a Möbius band. Some of these can be smoothly modeled in 3-dimensional space, and others cannot. Yet another example is the complete open Möbius band. Topologically, this is slightly different from the more usual — closed — Möbius band, in that any open Möbius band has no boundary.
Composed of a series of isosceles triangles gradually rotated around an ellipse, the building creates a dramatic division between interior and exterior while allowing the integration of public space into the center of the building by means of “the Infinite Patio.” The twisting of the structure also allows for three large vaulted spaces for the display of art objects.
The Möbius strip concept is also widely used in jewelry design.
The Euler characteristic of the Möbius strip is zero.