All About Klein Bottle



Klein bottle, topological space, named for the German mathematician Felix Klein, acquired by recognizing two closures of a barrel- shaped surface toward the path inverse that is important to get a torus. The surface isn't constructible in three-dimensional Euclidean space yet has intriguing properties, such as, being uneven, similar to the Möbius strip (q.v.); being shut, yet having no "inside" like a torus or a circle; and bringing about two Möbius strips if appropriately cut in two.