Felix Klein's work includes his famous "bottle", which irresistibly suggests a vessel that can be filled. Yet it is no bottle at all: originally, a German translator either made a slight mistake or perhaps intended a pun, translating Kleinsche Fläche as "Klein bottle" rather than "Klein surface" (in German, "bottle" is Flasche, while surface is Fläche).
The object was first described in 1882.
Like the Möbius strip (see the article *This Is Not a Möbius Strip!*), the Klein bottle is a topological curiosity. But while the Möbius strip has only one side, the famous bottle admits no distinction between its "inside" and its "outside".
The path traced by a moving circle
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It is now time to set the record straight. Viewed in three-dimensional space, Klein "surfaces" can also resemble the following illustration.
