Imaging maths - Inside the Klein bottle

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September 2003

Lawson-Klein bottle in S3

This model is large and may take a longer time to load.

JavaView Controls
Left-Mouse   Drag to rotate
s   Drag to scale
t   Drag to translate
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q   Stop auto-rotation
Right-Mouse   Show popup menu
Shift-s   Enable smooth drawing
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This is a projection of the Lawson-Klein bottle to 3-dimensional Euclidean space. The top region is clipped to provide better insight how the red and green Möbius band meet along the inner circle.

In fact, the surface is fully available and the degree of clipping may be interactively adjusted by varying the maximal scene bound in z-direction.

Open the camera inspector and adjust the maximal scene bound using

  • Right-mouse click, select Control Panel
  • In the region Clipping, enable the Scene and Z checkbox
  • Adjust the Z-Max slider

Interaction with the display can be accelerated by switching of the Texture and Transparency in the Material inspector, and the Z-Buffer in the Display inspector.

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  • Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.