64 Loops Reveal a Bottle With No Inside

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Can one continuous line reveal a bottle whose neck passes through its own wall?

The point follows 64 cross-sectional loops on the classical three-dimensional immersion of a Klein bottle. Its neck intersects the bottle wall before reconnecting, because a true Klein bottle cannot be embedded in three dimensions without self-intersection. The complete parametric system appears in the video.

Artismathic turns equations into visual art—one function at a time.

Music: 'Eternal Garden' by Dan Henig

#MathArt #KleinBottle #Topology