ORIENTABLE, ONE-SIDED SURFACE

 A connected surface is said to be orientable if the oriented triangle (ABC) included in this surface cannot be continuously transformed into coinciding with the triangle oriented in the opposite way (ACB); then, there are two types of orientations of triangles. In the non-orientable case, all the oriented triangles can be superimposed. For example, the "normal" strip opposite is orientable, whereas the Möbius strip is not. The triangle keeps its orientation. With each turn, the triangle changes orientation ("red green blue" becomes "red blue green" and vice-versa). Embedded in the Euclidian space , an orientable surface has two different faces, that can be painted in two different colors, which is not the case of non orientable, or one-sided, surfaces. In concrete terms, for a one-sided surface, an observer placed at a point M on a given side of the surface can cross it thanks to a continuous motion and find themselves at M on the opposite side. The "man" cannot cross to the opposite side. He can.